Oxidation of the heads is rarely a problem (the heads are made out of pretty stable materials that do not oxidize), but a buildup of oxide grime from floppy media is pretty common, along with dust bunnies and such. It's pretty much the same degradation mechanism that causes video and audio tape heads to gum up with use, and so the solutions are the same: A gentle clean.
In the case of the floppy drive, as mentioned previously, the chassis lube can turn gummy, and prevent proper operation. One of the failure modes is that the heads are thwarted from loading fully onto the media. Once you remove the drive, you'll be able to see very quickly whether this is the problem.
And yes, most of the problems are mechanical in nature, and are simply fixed. As long as no one violently yanked out a stuck floppy (an act that can rip the heads clear out), most drives are readily fixed.