There are only two very occasional issues I came across, both are related to software rather than hardware and are likely to be ironed out in future firmwares.
- After a (very) long period of being in Sleep Mode, often when simultaneously charged, the PSVita may "hang" and refuse to "wake up" despite the fact that the blue PlayStation button is lit up normally. To fix the problem, you hold down the Power button for a couple seconds until the system fully turns off and once it does, you release it, press it again and hold it until the recovery menu pops up. Once it does, select "Restart System".
- Again, after long periods of being in Sleep Mode, the screen may become unresponsive for a couple seconds after the system "wakes up". This is a rare issue which often goes away all by itself quickly, but if you want it to go away there and then, press the Power button to return to Sleep Mode and then the PlayStation button to "wake it back up" - works every time.
There's another slight problem with the system, but not all users will be affected by it since it relates to 3G. I don't know if it's just my carrier or not, but my PSVita often takes a long while to actually connect to the Internet via 3G. The system doesn't actually download anything before the 3G icon turns into the H icon, indicating an on-going HSDPA connection, followed by a swirl indicating that there's a transfer in progress. To speed up the process, and this perhaps only works in my head, I often return to the main menu of the system by pressing the PlayStation button, waiting for a few seconds and returning to the application, thinking that now that the CPU isn't as stressed, the transfer will go through more smoothly - this gives the impression of making the connection snappier.
The memory card or the SIM card got disconnected one time or two, but that's mostly because I keep my system in my bag at all times, so it's subjected to a lot of shaking over the course of my daily commute to and from the university - I don't think it's anything out of the ordinary. Another thing I do have to stress is
"keep the screen clean" - during gameplay you will inevitably cover it in dozens of fingerprints which can make touch detection go bonkers, at least that's what I'm blaming it on when it occasionally does.
Other than that, the system hasn't given me any problems. In its 11 months of service it certainly hasn't disappointed me so far - it's a very sturdy device and it can withstand the occasional fall, which is great when you're on-the-go - I don't think there's anything you should worry about, really. It's certainly the sturdies of all the handhelds I have, and I have quite a couple.