As an ACMT who fixes Apple laptops, desktops, and monitors allow me to offer some thoughts.
There were some 15" and 17" MBP models made around late 2007 to mid-2008 that had a defective nVidia graphics chip, and there is a special recall program in effect for that. The basic terms of the program are that it's good for four years from the date of purchase, in or out of warranty, Apple picks up the entire cost of the repair, and probably sends a bill to nVidia, but you don't care about that.
Then I think it was the Late 2008 model had some issues with the integrated graphics that would sometimes cause the display to flicker. The simple workaround for that was to switch to the discrete graphics, though that would eat into your battery life. There is a KB article on that, but there's no recall program like with the other issue. If your laptop fails the test, you have to pay for a new logic board. It should be covered under warranty if you managed to snag a system still under warranty.
Also, I'll just mention before I forget, that for over a decade now, Apple has soldered the CPU and GPU directly to the logic board, so if one goes out, the whole logic board has to be replaced.
That being said, I'd stay away from anything that's a 2007 model, that just seemed to be a really bad year for Apple quality wise.
The newer models, mid-2009 and onwards, have been pretty good quality wise. There's never one specific issue that keeps coming up over and over again. So I would go with the excellent suggestion of just checking Apple's refurb list and getting something from there. I doubt they'll have anything older than a mid-2010, which has been pretty solid across the board. The 2010 MacBook Airs might be the one exception, which have some issue with the logic board that Apple is very secretive about. It's covered under warranty, but they REQUIRE that the unit be shipped off to one of their repair depots, so that adds an extra day or two onto the repair time. Amusingly, they claim that sending it to the depot is to ensure that the repairs are done in a quick and timely fashion. Guess that's the Jobsian Reality Distortion Field in effect, but I digress.
I would definitely second the notion of buying a refurb from Apple. You never know if your logic board is going to crap out on you, but I can say that with the exception of the 2010 MacBook Airs, everything from at least Mid-09 has been pretty solid. If the logic board or something else does crap out on you, then you've got a full warranty, same as if you bought new. The two things Apple warranties do not cover, and Apple tend to be VERY strict about, are liquid damage, and physical abuse/accidental damage. You run the thing over with your car one morning, you're screwed. If you spill soda all over it, you're screwed. If you go to turn it on one day and find it won't power on, you're probably fine.