With your supplement, it should be kept cool and in the dark and replaced every six months or so as the ingredients can catalyze the breakdown of some of the vitamins in the supplement. Ideally whichever supplement you use should have either a made on/born on date or an expiration date. Any of the products that lack one of these dates should be avoided.
With regards to the retained skin, if it is loose you can remove it from the frog. It is possible that the skin simply tore and got stuck during the shedding process but it can also be indicative of a more serious condition such as chytridmycosis. If you suspect chytrid or another pathnogenic factor such as a fungal or protozoal infection, a skin scraping can help identify any problems and with chytrid there is now a PCR test that is very reliable in diagnosing the infection. If I remember correctly it is possible that vitamin deficiencies can result in skin problems but I would need to go dig in the literature to confirm this suspicion. As frogs tend to shed frequently, you can keep a close watch on the frog and see if it happens again (but this has its risks as some infections can kill a frog rapidly once something stresses the frog by disrupting the frogs ability to osmoregulate).
Another poteantial symptom would be if the frog is constantly sitting in the water bowl I would then suspect that there is a problem and seek the advice of a vet.
Ed