Irving, G. F., Freund-Levi, Y., Eriksdotter-Jonhagen, M., Basun, H., Brismar, K., Hjorth, E., Palmblad, J., Vessby, B., Vedin, I., Wahlund, L. O., and Cederholm, T. Omega-3 fatty acid supplementation effects on weight and appetite in patients with Alzheimer's disease: the omega-3 Alzheimer's disease study. J Am Geriatr Soc 2009;57(1):11-17. View abstract.

This systematic review and meta-analysis of clinical trials conducted on participants with clinical anxiety symptoms provides the first meta-analytic evidence, to our knowledge, that omega-3 PUFA treatment may be associated with anxiety reduction, which might not only be due to a potential placebo effect, but also from some associations of treatment with reduced anxiety symptoms. The beneficial anxiolytic effects of omega-3 PUFAs might be stronger in participants with specific clinical diagnoses than in those without specific clinical conditions. Larger and well-designed clinical trials should be performed with high-dose omega-3 PUFAs, provided as monotherapy and as adjunctive treatment to standard therapy.

An 18-month study was published in 2014 that evaluated how borage seed oil — rich in GLA — and fish oil rich fared against each other in treating patients with rheumatoid arthritis. It was discovered that all three groups (one taking fish oil, one taking borage oil and one taking a combination of the two) “exhibited significant reductions” in disease activity, and no therapy outperformed the others. For all three, “meaningful clinical responses” were the same after nine months. (11)
Gajos, G., Zalewski, J., Rostoff, P., Nessler, J., Piwowarska, W., & Undas, A. (2011, May 26). Reduced thrombin formation and altered fibrin clot properties induced by polyunsaturated omega-3 fatty acids on top of dual antiplatelet therapy in patients undergoing percutaneous coronary intervention (OMEGA-PCI Clot). Arteriosclerosis, Thrombosis, and Vascular Biology 111.228593. Retrieved from
Some people who are hypersensitive to fish or have a known allergy to fish products may have a negative reaction to fatty acids which were derived from fish. Some fish oil tablets are also produced with alpha-linolenic acids which come from nuts, which may aggravate those which have an allergy to these products. In many cases these allergies will manifest themselves as a skin rash, but the symptoms could be more severe depending on the severity of your allergies. People with this concern will need to avoid using these products.
“The review provides good evidence that taking long-chain omega 3 (fish oil, EPA or DHA) supplements does not benefit heart health or reduce our risk of stroke or death from any cause.  The most trustworthy studies consistently showed little or no effect of long-chain omega 3 fats on cardiovascular health. On the other hand, while oily fish is a healthy food, it is unclear from the small number of trials whether eating more oily fish is protective of our hearts. 
Jump up ^ Heartney, Eleanor (2007). "Zhang Huan: Becoming the Body". Zhang Huan: Altered States. Charta and Asia Society. ISBN 978-8881586417. Retrieved 2014-10-23. This becomes abundantly clear in the work of Chinese body artist Zhang Huan. In the course of his career, Zhang Huan has subjected himself to painful trials: sitting motionless for hours in an outhouse covered in honey and fish oil while flies crawled over his body [...].
Today the only Food and Drug Administration (FDA)-approved form of dietary omega-3 FA supplement is Lovaza (omega-3-acid ethyl esters; GlaxoSmithKline), which contains 375 mg of DHA and 465 mg of EPA per 1 g capsule. The myriad of dietary supplements of fish oil, including Kosher capsules, vary from comparable content to insignificant amounts, and for the most part can include other fats and cholesterols. In comparison, to achieve approximately 1 g of EPA and DHA in a meal, 12 ounces of canned light tuna, 2 to 3 ounces of sardines, 1.5 to 2.5 ounces of farmed Atlantic salmon, or 20 ounces of farmed catfish must be consumed (Table 1).65 Unfortunately, potentially high levels of harmful pollutants offset this source of omega-3 FA. The FDA action level for unacceptably high mercury content in fish is 1.0 μg/g. The mercury level in most fish is at or below 0.1 μg/g, but tilefish, swordfish, and king mackerel have high levels of mercury. The majority of fish species also contain <100 ng/g of polychlorinated biphenyls, which is below the FDA action level of 2000 ng/g. Dioxins, which do not have FDA action levels, are present in the majority of marine life.66

There is, however, significant difficulty in interpreting the literature due to participant recall and systematic differences in diets.[53] There is also controversy as to the efficacy of omega−3, with many meta-analysis papers finding heterogeneity among results which can be explained mostly by publication bias.[54][55] A significant correlation between shorter treatment trials was associated with increased omega−3 efficacy for treating depressed symptoms further implicating bias in publication.[55]
In later life, cognitive function and brain deterioration may become a concern. Once again, maintaining high levels of EPA has been shown to lower the risk of developing and worsening cognitive decline and dementia. If, however, you know someone who already has a diagnosis of dementia or Alzheimer’s, their brain has already been damaged and needs structural support. At this point, DHA becomes important again and taking a high-EPA product that contains 250mg of DHA also is important to prevent further loss of brain tissue.
High blood pressure. Fish oil seems to slightly lower blood pressure in people with moderate to very high blood pressure. Some types of fish oil might also reduce blood pressure in people with slightly high blood pressure, but results are inconsistent. Fish oil seems to add to the effects of some, but not all, blood pressure-lowering medications. However, it doesn't seem to reduce blood pressure in people with uncontrolled blood pressure who are already taking blood pressure-lowering medications.