Welcome to WP! And to WPCentral!
In my experience, the thing to look out for with used 920s is that many vendors, especially on eBay, refurbish the phone and use a cheap replacement chassis in the process. If you're not buying off of eBay, disregard.
A lot of people, myself included, experienced an issue with the chassis creaking at points. At first I thought this was a problem, but after seeing a video of a 920 being disassembled and reassembled, I realized that it's just because of the snug fit of the screen into the unibody chassis. The creaking only happened sporadically for the first few months of ownership, and now my phone only creaks if it gets really hot. It really bothers some other 920 owners, though. I thought I'd let you know beforehand so you didn't think that you had a major problem.
All of the other issues I can think of are not 920-specific and can happen to any phone: poor/damaged antennae, leading to poor call quality and/or dropped calls; battery won't accept a charge and/or discharges too quickly; the body isn't perfect so ehrmagerd I have to flame Nokia, MS, Ballmer personally and anyone else who crosses my path.
Oh, and you may not have an Instagram app. ;-) Enjoy your 920!