Additional side effects of fish oil supplements which have been reported include headache, short-term memory loss, depression, somatic disorders, and increased risk of colon cancer, nasopharyngitis, worsening of asthma symptoms, hemolytic anemia, decreased physical activity, increased appetite, a general uncomfortable feeling or increased blood pressure. The percentage of users that develop these side effects is not known. If these side effects become severe it is recommended that you stop using fish oil supplements.
To our knowledge, this is the first systematic review and meta-analysis to examine the anxiolytic effects of omega-3 PUFAs in individuals with anxiety symptoms. The overall findings revealed modest anxiolytic effects of omega-3 PUFAs in individuals with various neuropsychiatric or major physical illnesses. Although participants and diagnoses were heterogeneous, the main finding of this meta-analysis was that omega-3 PUFAs were associated with significant reduction in anxiety symptoms compared with controls; this effect persisted vs placebo controls. Furthermore, the association of treatment with reduced anxiety symptoms of omega-3 PUFA were significantly higher in subgroups with specific clinical diagnoses than in subgroups without clinical conditions.
In another study, Australian researchers looked at whether giving infants added omega-3 fatty acids might improve health,4 including reducing their risk for heart disease. They gave 420 infants either an omega 3 supplement or olive oil from birth through six months, then revisited that at age 5 years to see if either group appeared healthier from a heart risk point of view.
They also found that taking more long-chain omega 3 fats (including EPA and DHA), primarily through supplements probably makes little or no difference to risk of cardiovascular events, coronary heart deaths, coronary heart disease events, stroke or heart irregularities. Long-chain omega 3 fats probably did reduce some blood fats, triglycerides and HDL cholesterol. Reducing triglycerides is likely to be protective of heart diseases, but reducing HDL has the opposite effect. The researchers collected information on harms from the studies, but information on bleeding and blood clots was very limited. 
Hernandez, D., Guerra, R., Milena, A., Torres, A., Garcia, S., Garcia, C., Abreu, P., Gonzalez, A., Gomez, M. A., Rufino, M., Gonzalez-Posada, J., Lorenzo, V., and Salido, E. Dietary fish oil does not influence acute rejection rate and graft survival after renal transplantation: a randomized placebo-controlled study. Nephrol.Dial.Transplant. 2002;17(5):897-904. View abstract.
Preventing re-blockage of blood vessels after angioplasty, a procedure to open a closed blood vessel. Research suggests that fish oil decreases the rate of blood vessel re-blockage by up to 45% when given for at least 3 weeks before an angioplasty and continued for one month thereafter. But, when given for 2 weeks or less before angioplasty, it doesn't seem to have any effect.