We've had a number of these machines pass through werk. The 600/E/X/N machines all seemed to kill their respective batteries before time. The T20/1 machines all seem to have slightly iffy displays and kill their hard disks.
I should kick off my saying the Thinkpad (or Stinkpad, as I've seen it called) is a great brand, and as a sysadmin, I'm really pretty pleased with them. They're pretty solid, pretty reliable, work well, and are backed by sensible support. All that, and they don't cost the earth.
As for the problems with them, this is of course highly subjective. I don't have any hard facts, but my werk has had around 20-30 laptops at any one time, mostly of similar ranges.
We shrunk a bit a while back, so sold off a whole load of 600 range Thinkpads to the staff. To the best of my knowledge, only four or five machines (of 20 odd) had working batteries (after around 2-3 years use each). Since then, I think all of those have failed. So, IBM 600 range Thinkpads seem to kill off their batteries, even if you don't run the machine on batteries very often. There seems to be a design flaw, although IBM haven't acknowledged it yet (even with latest BIOS upgrades, the problem still seems to exist).
As for the T21, the batteries also tail off after a while. Most of our T20 series machines are about two to three years old now. A good number of them are perfectly good, so definitely have better batteries/chargers than the 600 range. But, just about all of out T20 range have marks on the displays. My guess is that the protective layer in the lid, that shields the TFT and backlight layers from impact are a bit thin. The displays have slight variances in the brightness at a few points, which makes me wonder if it's because the machine got stuffed into a bag or something, distorting the various layers of the lid, and so leaving marks.
Also, a number of our T20 series machines have had failing hard disks. I originally thought this problem only affected the 15GB disks, but we've just had a 20GB disk fail too. IBM handily point you to a Drive Fitness Test (DFT) program, which is pretty good at finding problems (although not on the last two disks we've had fail). Oh, when I say fail, I mean "slow down", "clatter", "squeek", etc etc. We've had a few dodgy sectors, but by and large, no disks stopped spinning, so we've always been able to backup data before replacing the disks.
IBM have streamlined disk replacement too, it seems. Provided you convince them there's a problem, they'll just ship out a replacement; when the courier hands it over, you hand over the old one. Very easy, and I have to say much appreciated.
We've just bought a couple of T40s (which I've talked about before. We're about to take delivery of a whole load more, which will pretty much see the end of all of our remaining 600X and T20/1 machines. I wonder what "the thing" will be when we've been using them for a while...?