[Only Toyota for me]

Don't know of any problems to look for around the 2000 model year, other than the sludge problems toyota had around that time. I don't know if the corolla's were affected or not.
I had a 2000 geo prizm (same car) that i bought used with 80k miles for $4000 just over a year ago. Nice car & was fairly reliable except for the fact that it used quite a bit of oil between changes. I think the reason is cause the previous owner used it while on their lds mission, and didn't change the oil often enough or not at all.
I did have to change the plug wires on it because it had a hesitation when accelerating.
Other than that, pretty reliable cars & i'd recomend them highly. They've been known to go 450k plus miles with the same engine & tranny.