Probably the onboard storage. It uses flash-memory, sort of like the memory cards GCN used, except you can't just swap it out easily if it corrupts. And supposedly they can only be saved to so-many times before they corrupt, and then you'd be shipping in upwards of 75 bucks(or more) without warranty to get it replaced...and an extra 75 bucks would probably get you a new Wii easily. Although I'm not sure if any of the new Wiis being sold still have GCN support or not, if you cared for it.
Well that's mostly what I'd worry about. Maybe the condition of the disc-drive since mine sometimes sputters if I haven't used it for a few months(maybe dust gets into it, I dunno). Otherwise the Wii is a pretty solid little machine, so unless they modded it or corrupted the memory before turning it into GS, it should be fine mostly. But you just never know how long that flash-memory is going to last..