Hey J-Raud, welcome aboard!
The biggest problem with the Bandit 400 is the fact that they haven't been imported into the States since 1993 (assuming thats where you are). Parts are fairly hard to come by anymore, which is why a lot of us have made it our business to see what else will fit on there.
More than likely if you find one in non-running condition it will have one of two problems, if not both. Either the carburators will be gummed up and filthy, or there will be an electrical fault. The electrical problem is the worst, since if the Digital Ignition Box is fried, you are in a lot of trouble. Some people have had decent luck repairing them, but it seems to be a 50/50 chance. The carburators are a lot of fun as well, since they are also not particularly easy to get parts for and there are just some shops who will refuse to touch them.
As for the engines themselves, they are fairly reliable. Most problems you'll run across can be summed up as either carburation or electrical. Of course, before purchasing you'll want to get a compression test on the bike if at all possible.
Probally your best bet is to find a bike with decent compression, a wiring harness that doesn't look like a rats nest of mismatched cables, and spark. Compression and spark will be the most difficult to check for, you'll need a compression gauge. Luckily, since the sparkplug has to come out to screw the gauge in, you can also check spark at this time. Bring your own known-good plug!
Other than that, the standard stuff applies. Check the brakes, look for anything that appears to be leaking, check inside the gas tank for rust (which you -will- find, the question is going to be 'is it fixable' here), and the like.
Honestly, your best bet will be to find one thats cosmetically rough, but runs. Since you are looking for a project bike, don't fear leaky suspensions! There are plenty that will fit on there as 'upgrades'