The one word answer is no. It's totally safe and experts are recommending it, even to young children. In the past, due to poor (or no) quality controls, fish oil was found to contain toxic chemicals and heavy metals such as PBC's and mercury from contaminated fish sources. This is no longer a problem due to standardized testing.
Unless you are taking ver y high doses of fish oil (which may be harmful as it might interact with blood thinners) it doesn't cause any problems except for some possible minor side effects, such as stomach complaints.
Most people commonly take 1 to 3 grams of fish oil daily. No harmful side effects has been reported by scientific studies at this dosage range.
Higher doses have been safely used in clinical trials as well.