To avoid fish oil supplements containing mercury or other harmful contaminants, purchase supplements from a reputable source that clearly tests for these health-hazardous contaminants in its products. These tests should be ideally conducted by a third-party, and a certificate of analysis should indicate the levels of purity from environmental toxins.

Good points, Miroslav. Focusing on your 4th point, with so many different formulations on the market that contain various preservatives, only looking at the blood levels of omega-3’s as the flag for increased risk for prostate cancer tends to ignore the fact that certain populations in coastal regions maintain a diet high in omega fish oils and don’t have a marked increase level of prostate cancer, pointing to the fact that another agent may be to blame here.

The #1 Pharmacist Recommended Omega-3/Fish Oil brand,* Nature Made fish oil supply comes from deep ocean waters, not farm-raised fish. State-of-the-art purification processes remove mercury and ensure high levels of fish oil purity and concentration, guaranteed to pass the stringent standards of the Global Organization for EPA and DHA Omega-3 Voluntary Monograph.‡
Is krill oil better than fish oil for omega-3? Krill oil and fish oil are popular dietary supplements containing omega-3. Krill oil comes from a small crustacean while fish oil comes from oily fish, such as salmon. Both are shown to increase blood levels of omega-3 and have benefits for health. Learn more about the differences between krill oil and fish oil here. Read now
Although results from studies regarding the disease processes of AD seem to be promising, there are conflicting data regarding the use of omega-3 fatty acids in terms of cognitive function. Neuropsychiatric symptoms accompany AD from early stages and tend to increase with the progression of the disease (55). An analysis of 174 patients randomized to a placebo group or to a group with mild to moderate AD (MMSE score ≥15) treated with daily DHA (1.7 g) and EPA (0.6 g) found that at 6 mo, the decline in cognitive function did not differ between the groups. Yet, in a subgroup with very mild cognitive dysfunction (n = 32, MMSE score >27), they observed a significant reduction in the MMSE decline rate in the DHA+EPA-supplemented group compared with the placebo group (47). Another study that looked at DHA supplementation in individuals with mild to moderate AD used the Alzheimer's Disease Assessment Scale–Cognitive subscale, which evaluates cognitive function on a 70-point scale in terms of memory, attention, language, orientation, and praxis. This study found that DHA supplementation had no beneficial effect on cognition during the 18-mo trial period for the DHA group vs. placebo (56).
ALA is an essential fatty acid, meaning that your body can’t make it, so you must get it from the foods and beverages you consume. Your body can convert some ALA into EPA and then to DHA, but only in very small amounts. Therefore, getting EPA and DHA from foods (and dietary supplements if you take them) is the only practical way to increase levels of these omega-3 fatty acids in your body.
People with metabolic syndrome (the combination of central obesity, high blood pressure, disturbed lipid profile, and impaired glucose tolerance) are at increased risk of death from cardiovascular disease, diabetes, cancer, and other apparently “age-related” disorders. Because metabolic syndrome is closely associated with chronic low-grade inflammation, the powerful anti-inflammatory effects of omega-3 fats are especially important as a means of slowing or stopping the progression of this deadly disorder.
Most Americans take in far more of another essential fat—omega-6 fats—than they do omega-3 fats. Some experts have raised the hypothesis that this higher intake of omega-6 fats could pose problems, cardiovascular and otherwise, but this has not been supported by evidence in humans. (4) In the Health Professionals Follow-up Study, for example, the ratio of omega-6 to omega-3 fats wasn’t linked with risk of heart disease because both of these were beneficial. (5) Many other studies and trials in humans also support cardiovascular benefits of omega-6 fats. Although there is no question that many Americans could benefit from increasing their intake of omega-3 fats, there is evidence that omega-6 fats also positively influence cardiovascular risk factors and reduce heart disease.

Fish or seafood allergy: Some people who are allergic to seafood such as fish might also be allergic to fish oil supplements. There is no reliable information showing how likely people with seafood allergy are to have an allergic reaction to fish oil. Until more is known, advise patients allergic to seafood to avoid or use fish oil supplements cautiously.

Ozaydin, M., Erdogan, D., Tayyar, S., Uysal, B. A., Dogan, A., Icli, A., Ozkan, E., Varol, E., Turker, Y., and Arslan, A. N-3 polyunsaturated fatty acids administration does not reduce the recurrence rates of atrial fibrillation and inflammation after electrical cardioversion: a prospective randomized study. Anadolu.Kardiyol.Derg. 2011;11(4):305-309. View abstract.
Even healthy oils form trans fats when heated. Each oil has a different temperature at which it forms its own trans fats. Generally, when the oil begins to smoke is when trans fats are formed. Did this study consider how and at what temperatures the fish were cooked? Are some of the suppliments heated before being made into capsules? Did it also consider that many types of fish have dangerous levels of mercury?

A 2012 study involved children from 6 to 12 years of age with ADHD who were being treated with methylphenidate and standard behavior therapy for more than six months. The parents of these children reported no improvement in behavior and academic learning using these standard treatments. The researchers randomly gave some of the children an omega-3 and omega-6 acid supplementation or a placebo. They found “statistically significant improvement” for the omega group in the following categories: restlessness, aggressiveness, completing work and academic performance. (5)

So back to fish oil in general. The major fish oil benefits include decreasing the risk of heart disease and stroke while also helping reduce symptoms of depression, hypertension, attention deficit hyperactivity disorder (ADHD), joint pain, arthritis and chronic skin ailments like eczema. (2) Fish oil intake has also been associated with aiding the body in weight loss, fertility, pregnancy and increased energy. Prescription fish oil has even been approved by the FDA to lower unhealthy high triglyceride levels. (3)
Additionally, total polychlorinated biphenyl (PCB) content was measured in every product. All product recorded PCB levels within the Food and Drug Administration’s (FDA) 2 PPM limit for the edible parts of fish/shellfish as well as the stricter standards enacted by California’s Proposition 65, which requires products containing greater than 0.09 PPM of PCB content to bear a cancer warning. The worst offender, Now Foods Ultra Omega-3 Fish Oil, recorded 0.04 PPM of PCB content.
A study published in Brain Research shows how far-reaching fish oil can be for people with diabetes. Researches found that fish oil can help reduce the risk of diabetics from developing cognitive deficit because it protects the hippocampus cells from being destroyed. The study also showed that fish oil could help reduce oxidative stress, which plays a central role in the development of diabetes complications, both microvascular and cardiovascular. (22)
It exists in nature in three forms, one derived from land plants and two derived from marine sources. In the body, omega-3 is highly concentrated in the brain; it is critical to the formation and maintenance of nerve cell membranes. Research shows that in the nervous system, omega-3s foster the development of brain circuitry and the processing of information. They also play important roles in stabilizing mood and staving off cognitive decline. Low levels of omega-3s are linked to poor memory and depression. Omega-3 fats are also critical for the formation of anti-inflammatory molecules in the body.
In your final paragraph, you suggest that a ratio of 2:1 EPA/DHA maybe best for reducing inflammation. Are you suggesting using two separate products to obtain that ratio? I can't see how it is achieveable through standard omega-3 products. Good fish oil brands are typically 60% or higher EPA, but never reach a 2:1 ratio in my product searches. According to case studies (link below), 1 gram of EPA per day (60% or more of the total omega-3 content) is sufficient and the highest efficacy.
Heavy metal poisoning by the body's accumulation of traces of heavy metals, in particular mercury, lead, nickel, arsenic, and cadmium, is a possible risk from consuming fish oil supplements.[medical citation needed] Also, other contaminants (PCBs, furans, dioxins, and PBDEs) might be found, especially in less-refined fish oil supplements.[citation needed] However, heavy metal toxicity from consuming fish oil supplements is highly unlikely, because heavy metals selectively bind with protein in the fish flesh rather than accumulate in the oil. An independent test in 2005 of 44 fish oils on the US market found all of the products passed safety standards for potential contaminants.[107][unreliable source?]
Matsumura  K, Noguchi  H, Nishi  D, Hamazaki  K, Hamazaki  T, Matsuoka  YJ.  Effects of omega-3 polyunsaturated fatty acids on psychophysiological symptoms of post-traumatic stress disorder in accident survivors: a randomized, double-blind, placebo-controlled trial.  J Affect Disord. 2017;224:27-31. doi:10.1016/j.jad.2016.05.054PubMedGoogle ScholarCrossref
Unsafe for children. Fish oil supplements are not considered safe for children. Too much of this fat in their system can lead to a chemical imbalance in the brain which could stunt healthy growth and development. Because of this, and the possible exposure to polychlorinated biphenyls, methylmercury and other toxins which are found in some sources of fish, it is not recommended that women who are pregnant take excessive amounts of fish oil. Servings of fish should be limited to six ounces per week and they should refrain from using fish oil or other fatty acid supplement pills. Children should not consume more than two ounces of fish per week to avoid overexposure to these chemicals. Now you know although fish oil can benefit human beings a lot, fish oil side effects should never be neglected for the sake of your safety. 
Sangiovanni, J. P., Agron, E., Meleth, A. D., Reed, G. F., Sperduto, R. D., Clemons, T. E., and Chew, E. Y. {omega}-3 Long-chain polyunsaturated fatty acid intake and 12-y incidence of neovascular age-related macular degeneration and central geographic atrophy: AREDS report 30, a prospective cohort study from the Age-Related Eye Disease Study. Am J Clin Nutr 2009;90(6):1601-1607. View abstract.
Sangiovanni, J. P., Agron, E., Meleth, A. D., Reed, G. F., Sperduto, R. D., Clemons, T. E., and Chew, E. Y. {omega}-3 Long-chain polyunsaturated fatty acid intake and 12-y incidence of neovascular age-related macular degeneration and central geographic atrophy: AREDS report 30, a prospective cohort study from the Age-Related Eye Disease Study. Am J Clin Nutr 2009;90(6):1601-1607. View abstract.
The chemical structures of EPA and DHA are very similar and they compete for uptake and processing resources. During digestion, the triglyceride molecules in standard fish oil are broken down into a mono glycerol and two free fatty acids, small enough to be absorbed into cells of the gut lining. More often than not, DHA is the fatty acid that remains attached to the glycerol backbone, meaning in essence that DHA gets a ‘free pass’ into the gut, while the remaining free fatty acids (more often EPA) must reattach onto a glycerol molecule or risk being oxidised and used as fuel. The implication of this is that DHA levels in our cells are often concentrated at the expense of EPA after absorption when taking EPA and DHA in the standard ratio of 1.5 to 1.
Fortier, M., Tremblay-Mercier, J., Plourde, M., Chouinard-Watkins, R., Vandal, M., Pifferi, F., Freemantle, E., and Cunnane, S. C. Higher plasma n-3 fatty acid status in the moderately healthy elderly in southern Quebec: higher fish intake or aging-related change in n-3 fatty acid metabolism? Prostaglandins Leukot.Essent.Fatty Acids 2010;82(4-6):277-280. View abstract.
Five studies with 7 data sets recruited participants without specific clinical conditions.36,47,51,55,60 The main results revealed that there was no significant difference in the association of treatment with reduced anxiety symptoms between patients receiving omega-3 PUFA treatment and those not receiving it (k, 5; Hedges g, –0.008; 95% CI, –0.266 to 0.250; P = .95) (Figure 3A). Fourteen studies with 14 data sets recruited participants with specific clinical diagnoses.33-35,48-50,52-54,56-59,61 The main results revealed a significantly greater association of treatment with reduced anxiety symptoms in patients receiving omega-3 PUFA treatment than in those not receiving it (k, 14; Hedges g, 0.512; 95% CI, 0.119-0.906; P = .01) (Figure 3A). Furthermore, according to the interaction test, the association of omega-3 PUFA treatment with reduced anxiety symptoms was significantly stronger in subgroups with specific clinical diagnoses than in subgroups without specific clinical conditions (P = .03).
Children: Fish oil is POSSIBLY SAFE when taken by mouth appropriately. Fish oil has been used safely through feeding tubes in infants for up to 9 months. But young children should not eat more than two ounces of fish per week. Fish oil is also POSSIBLY SAFE when given in the vein by a health care professional to infants who cannot take food by mouth. Fish oil is POSSIBLY UNSAFE when consumed from dietary sources in large amounts. Fatty fish contain toxins such as mercury. Eating contaminated fish frequently can cause brain damage, mental retardation, blindness and seizures in children.