Attention deficit-hyperactivity disorder (ADHD) in children. Early research shows that taking fish oil improves attention, mental function, and behavior in children 8-13 years-old with ADHD. Other research shows that taking a specific supplement containing fish oil and evening primrose oil (Eye Q, Novasel) improves mental function and behavior in children 7-12 years-old with ADHD.
Ramakrishnan, U., Stein, A. D., Parra-Cabrera, S., Wang, M., Imhoff-Kunsch, B., Juarez-Marquez, S., Rivera, J., and Martorell, R. Effects of docosahexaenoic acid supplementation during pregnancy on gestational age and size at birth: randomized, double-blind, placebo-controlled trial in Mexico. Food Nutr Bull 2010;31(2 Suppl):S108-S116. View abstract.
Bo and I worked with Dr. Harris many years ago to measure the impact of eating one Omega Cookie® daily on the study participants’ omega-3 index levels, and we recently ran into him at ISFFAL. At the conference, we remeasured our omega-3 index and omega-6/omega-3 ratios, and a few weeks later, we got our results in the mail. For the two of us, it was exciting to get another concrete measure of how our daily omega-3 consumption impacted our scores. For the record, we take one vial of Omega Restore™ per night and frequently sneak an Omega Heaven® or Omega Cookie during the day.
We’ve written about the dose necessary to achieve measurable benefits before. However, a person’s actual omega-3 intake can be tricky to estimate. Even if you eat at least two servings of fatty fish per week, as the American Heart Association recommends (10), your fish might contain more or less omega-3s depending on the fish species, the time of year, and how you cook it. Even taking fish oil supplements isn’t always straightforward, as dose can be impacted by numerous bioavailability factors, as well as genetics, age, gender, medication-use and lifestyle.
Weight loss. Some research shows that eating fish improves weight loss and decreases blood sugar in people who are overweight with high blood pressure. Early research also shows that taking a specific fish oil supplement (Hi-DHA, NuMega) lowers body fat when combined with exercise. But other evidence suggests that taking another specific fish oil supplement (Lovaza) does not lower body weight in overweight people.

Marchioli, R., Barzi, F., Bomba, E., Chieffo, C., Di, Gregorio D., Di, Mascio R., Franzosi, M. G., Geraci, E., Levantesi, G., Maggioni, A. P., Mantini, L., Marfisi, R. M., Mastrogiuseppe, G., Mininni, N., Nicolosi, G. L., Santini, M., Schweiger, C., Tavazzi, L., Tognoni, G., Tucci, C., and Valagussa, F. Early protection against sudden death by n-3 polyunsaturated fatty acids after myocardial infarction: time-course analysis of the results of the Gruppo Italiano per lo Studio della Sopravvivenza nell'Infarto Miocardico (GISSI)-Prevenzione. Circulation 4-23-2002;105(16):1897-1903. View abstract.
Egert, S., Somoza, V., Kannenberg, F., Fobker, M., Krome, K., Erbersdobler, H. F., and Wahrburg, U. Influence of three rapeseed oil-rich diets, fortified with alpha-linolenic acid, eicosapentaenoic acid or docosahexaenoic acid on the composition and oxidizability of low-density lipoproteins: results of a controlled study in healthy volunteers. Eur J Clin Nutr 2007;61(3):314-325. View abstract.
The short answer is no. There are many websites which advise people to stop eating vegetable oils and switch to fish oil in order to increase their intake of omega-3 fatty acids. Fish oil is a good source of omega-3 essential fatty acids and should be consumed, but that doesn’t necessarily mean that one should completely replace vegetable oils with fish oil.
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.

The effect of fish oil consumption on prostate cancer is controversial,[28][29] as one study showed decreased risk with higher blood levels of DPA, whereas another reported increased risk of more aggressive prostate cancer with higher blood levels of combined EPA and DHA.[30] Some evidence indicated an association between high blood levels of omega-3 fatty acids and an increased prostate cancer risk.[31]
Omega-3s have been studied for other conditions, with either inconclusive or negative results. These conditions include allergies, atopic eczema (an allergic skin condition), cystic fibrosis, diabetes, inflammatory bowel diseases (Crohn’s disease or ulcerative colitis), intermittent claudication (a circulatory problem), nonalcoholic fatty liver disease, and osteoporosis. 
To evaluate the potential placebo effect, we made further subgrouping analyses. In the subgroups of studies using placebo controls, the omega-3 PUFAs still revealed a consistent positive anxiolytic association with anxiety symptoms. These phenomena meant that the anxiolytic effect of omega-3 PUFAs is probably not entirely owing to the placebo effect.
If you get your omega-3 index measured, you’ll know if your current efforts are sufficient. And this knowledge is especially important given that even health-conscious people are not always self-aware. One survey found that in a group of people with omega-3 index levels in the intermediate risk range, some 30% believed they were consuming enough omega-3s (11). One registered dietitian wrote a compelling story about exactly this experience. She discovered she was in the intermediate range, in spite of her intentions to eat enough fish.

And in osteoarthritis, when a DHA/EPA formulation was added to chondroitin sulfate, people experienced more complete relief of symptoms such as stiffness and pain. One study found a significant increase in walking speed in people who supplemented with fish oil versus those who did not.79,80 As with the beneficial results seen in people with bone loss, these positive findings may have been the result of the decreased inflammatory destruction of joint cartilage.81
Dioxins and PCBs may be carcinogenic at low levels of exposure over time. These substances are identified and measured in one of two categories, dioxin-like PCBs and total PCBs. While the U.S. FDA has not set a limit for PCBs in supplements, the Global Organization for EPA and DHA (GOED) has established a guideline allowing for no more than 3 picograms of dioxin-like PCBs per gram of fish oil. In 2012, samples from 35 fish oil supplements were tested for PCBs. Trace amounts of PCBs were found in all samples, and two samples exceeded the GOED‘s limit.[52] Although trace amounts of PCBs contribute to overall PCB exposure, claims the amounts reported by tests it ordered on fish oil supplements are far below those found in a single typical serving of fish.[52]

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
Both omega−6 and omega−3 fatty acids are essential: humans must consume them in their diet. Omega−6 and omega−3 eighteen-carbon polyunsaturated fatty acids compete for the same metabolic enzymes, thus the omega−6:omega−3 ratio of ingested fatty acids has significant influence on the ratio and rate of production of eicosanoids, a group of hormones intimately involved in the body's inflammatory and homeostatic processes, which include the prostaglandins, leukotrienes, and thromboxanes, among others. Altering this ratio can change the body's metabolic and inflammatory state.[16] In general, grass-fed animals accumulate more omega−3 than do grain-fed animals, which accumulate relatively more omega−6.[86] Metabolites of omega−6 are more inflammatory (esp. arachidonic acid) than those of omega−3. This necessitates that omega−6 and omega−3 be consumed in a balanced proportion; healthy ratios of omega−6:omega−3, according to some authors, range from 1:1 to 1:4.[87] Other authors believe that a ratio of 4:1 (4 times as much omega−6 as omega−3) is already healthy.[88][89] Studies suggest the evolutionary human diet, rich in game animals, seafood, and other sources of omega−3, may have provided such a ratio.[90][91]
Bianconi, L., Calo, L., Mennuni, M., Santini, L., Morosetti, P., Azzolini, P., Barbato, G., Biscione, F., Romano, P., and Santini, M. n-3 polyunsaturated fatty acids for the prevention of arrhythmia recurrence after electrical cardioversion of chronic persistent atrial fibrillation: a randomized, double-blind, multicentre study. Europace. 2011;13(2):174-181. View abstract.

A March 2010 lawsuit filed by a California environmental group claimed that eight brands of fish oil supplements contained excessive levels of PCB's, including CVS/pharmacy, Nature Made, Rite Aid, GNC, Solgar, Twinlab, Now Health, Omega Protein and Pharmavite. The majority of these products were either cod liver or shark liver oils. Those participating in the lawsuit claim that because the liver is the major filtering and detoxifying organ, PCB content may be higher in liver-based oils than in fish oil produced from the processing of whole fish.[63][64]
Abnormal rapid heart rhythms (ventricular arrhythmias). Population research suggests that eating a lot of fish has no effect on the risk for abnormal rapid heart rhythms. Clinical research is inconsistent. Some research shows that taking fish oil daily does not affect the risk for abnormal heart rhythms. But other research shows that taking fish oil for 11 months delays the development of the condition. However, overall, taking fish oil does not seem to reduce the risk of death in people with abnormal rapid heart rhythms.