Haven't had any issues with the pre-owned PS2 Slim I've had since 2008 (despite it having been dropped to the floor about 3 times, while on and with a spinning disc inside), except that Quake 3 Revolution barely works on it, but that was a used game I got from GameStop, and despite replacing it 3 times I always get discs that look like they've been rubbed against sand paper, so I don't think these problems were the fault of my PS2.
Just bought a second PS2 Slim, not pre-owned this time, and it'll be interesting to see if it will outlive the PS3 I bought last month.