A. Horav Shlomo Miller Shlit’a pointed out that in principle there are different reasons why vitamins or medicines may be permitted even without supervision. 1) They may have an unpalatable or unpleasant flavour and therefore considered “Nosen Taam Lifgam” that when mixed is permitted (See Pri Megodim’s introduction to Basar Vechalav). 2) During the manufacturing process the prohibited ingredients undergo a chemical transformation that turns them into something different, (See Remo Y.D. 67: 10 and Shach ibid. 33). 3) The prohibited items may be minimal and are annulled, at least Biblically. 4) Although not a generally accepted reason, some add as an argument the fact that they are not consumed in the normal way that food is eaten, but rather swallowed (Divrei Chaim Y.D. 2: 52).Therefore historically, there were and are Poskim that are lenient on vitamins when dealing with the ill or when in need. On our enquiry to the COR, Rabbi Tzvi Heber replied: Vitamins in a hard pill bitter format might be considered shelo k’derech achila and therefore permitted for someone who takes them for medicinal value (choleh).
In reality today, when consuming vitamins we must be concerned with many issues such as the raw ingredients, fillers, binders, lubricants, coating agents, flavors and the manufacturing process. Questionable ingredients include stearates (animal origin), lactose (dairy), fish oils, clams, eggs, gelatin (animal/fish derived) etc. There are also starches, alcohol & gluten etc. which are concerns for Passover use. Some may have a dairy & meat derived product in the same item, which is another concern; meat & milk together.
Therefore, although in principle there are valid reasons to be lenient when in need, in actuality they are complex and vary often from case to case. And since vitamins with kosher supervision are readily available these days, one should consume them. Please note that chewable vitamins, and the ones coated with a pleasant tasting coating, require reliable certification.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a