Supplement side effects vary - and it depends on the supplement. It's ideal if you can discuss a specific supplement with your doctor and find out what those side effects can be - because some are known.
If you were to take a certain dosage of a prescribed medication, your doctor would know your weight, gender, etc., and some of that knowledge, and knowledge of the drug's interactions, would go into deciding the dosage you would use and how long you would take the drug. When you buy an over-the-counter nutritional supplement, that is not a consideration.
I asked my doctor to run some tests on my blood last year and he discovered that although I have normal blood count, hemoglobin, etc., I was slightly anemic. (I eat a vegetarian diet most of the time.) He told me to take a certain dosage of a simple iron supplement and only take it for a short time - I think it was two months. It's not even a good idea to take that low-dosage iron long-term, so imagine if I thought taking daily for the rest of my life would have been a wise choice! Unless some health condition or illness requires it, it actually would be BAD for my health.
That's just an example but it's specific. Which is why talking to your doctor about side effects of a certain supplement is important.
' Unlike Canada, Germany, and France, the United States regulates dietary supplements similarly to foods, and does not require premarketing approval of safety, nor does the burden of proof rest on the manufacturer.'
- from Dietary Supplements - Complementary and Alternative Medicine in the United States - NCBI Bookshelf
'As a result of their pharmacological properties, dietary supplements, particularly botanical products, carry a risk of adverse effects and interactions. Unlike vitamins and minerals, herbal supplements are composed of many active compounds, and often, the primary active ingredient is unknown. Without knowing the active ingredient(s), it is a challenge for manufacturers to set standards that bear any therapeutic meaning. As such, consistency and quality checks throughout the manufacturing process garner even more importance (Berman and Straus, 2004).'
(The above is about the lack of standards with any 'therapeutic meaning.' What the effect of taking a certain supplement for 5 years , for example, in a certain dosage is another matter. Drug companies are required to list all the possible side effects. Supplement companies are not subject to the same requirements.)