The common headphone jack issue is that one of the pins comes loose very easily but that's a very simple fix of adding some extra solder. Beyond that the audio port gradually gets looser to the point headphones will very easily fall out; I think if you just never remove the headphones this will be much less likely to happen.
The main failures I've seen on eBay are: - dead battery (these are often in amazing condition otherwise because they were bought and hardly used) - loose audio jack (simple solder fix but may have the looseness issues) - broken membrane buttons (probably not very fixable?) - faded screen (probably has lots of other issues but generally usable)