About buying a particular D3, I'm not aware of any common issue or failure. I think it's going to be you have to evaluate it like any other older camera, test functions and be thorough and then take your chances.
About buying any D3, I do think there is a weak point now. I recently shot an event alongside someone who was shooting a D3. At 3200 and 6400, their shots looked awful, by today's standards. Skin tones and dynamic range were awful and noise was obvious. When I first saw the published shots, I thought they had been taken with a cellphone. For not much more money than you're talking, you could get a refurbished D610, possibly even for the same money get one used. The D610 is hardly my favorite camera in Nikon's lineup, but my point is that unless you need 9 fps or want the bigger pro body of the D3, I'd have a hard time buying a D3 now based on the performance. With a D610 for example, you would get vastly better ISO performance, better AF, a pop-up flash, video. It's a more versatile, current, better all-around camera. Don't get me wrong, I love my D3S, and I have a lot of (nostalgic) love for the D3. But for the money you're talking about, I'd prefer another camera for almost any subject.