The main thing is that it has been repaired properly and not botched, stolen recovered can still mean it was damaged.

Also check for stuff like history as often this gets lost between the original owner, insurance companies and salvage yards so you may have no paperwork or spare key for the car.

Make sure it is cheaper than non damaged, as when you come to sell it, it will need to be cheaper than non damaged.

In general though they can be a decent way to get a nice car for less money and nobody but you knows.

Look out for people claiming cars to be cat D when they are actually cat C and hope you wont bother to check.