The Background
The mollies you are most likely to buy at the pet store are hybrids. Black mollies, golden mollies, veiltail mollies, balloon mollies, and all the others are all hybrids created by careful cross-breeding of two or more species. Some molly species live in fresh water, while others live in brackish water. There's usually a little of both kind in any given aquarium strain.
The Problem
When mollies are kept in freshwater tanks, they often become sickly. Common symptoms are fin-rot, fungus, and the "shimmies". Fin-rot is a gradual decay of the fins, often with obviously dead, grey patches on the fins. Left untreated, this will kill your fish. Fungus usually looks like fine white threads and can appear anywhere on the body, though it's most common on the fins. Again, untreated, this is serious. Both fin-rot and fungus are easily treated with over-the-counter fish medicines. The shimmies are, as the name suggests, a bit like the dance of the same name. The fish seem to tread water, wobbling from side to side. Yet again, left untreated, this will kill your fish.