Hi Adam, I have a 2001 Prius now with 87k miles and do not hesitate to recommend it as a used car. For the things you mentioned:
Uneven tire wear - Inflate tires above Toyota's recommendation and (possibly) get the front end aligned. This one's really easy.
Steering shakes - There is a Toyota warranty extension for this for 5 years after the vehicle's original in-service date (this date draws nigh). Given the choice between multiple used Prius, I would prefer one that had steering rack already been replaced.
Transmission failure - Very approximately I have heard of about 10 failures in all the internet groups; all Prius years. Overall, this may total 10,000 vehicles in service. Typically Toyota has paid in part or all. It would certainly be a serious matter later, and were it mine I would be looking at replacing with the entire assembly from a dismantled vehicle. One member of the Yahoo technical group is actively trying to understand the potential role of fluid contamination in these failures.
The things you didn't mention:
High-voltage battery - once again, about 10 failures reported, and most covered by Toyota. Again the salvage dismantlers may eventually be our friends. As a buyer of a used 2001-2003 Prius you should confirm that the SSC 40G battery resealing has been done.
Error messages on the screen yet the car drives normally - I believe this to be the most common issue with Prius of the era. Relates to technical service bulletin EG011-03, most often resolved by replacing the engine control module (ECM) with one with new programming. See if this TSB has been performed. If not, the vehicle is on the "candidate" list.
Brake component corrosion - Ironically, as Prius' friction brakes are not used much, there can be corrosion in places with winter road salt. A competent inspection before purchase would resolve any questions.
Accelerator pedal - One of my Prius hobbies! A few of these go bad and the whole assembly is $200-$300 new. But what appears to go wrong is just "noisy" potentiometers and/or poor electrical contacts. I have just received another one of these to fix, having given my original one in trade. I am driving on a repaired one, and have been for about 7k miles. Only seems worth mentioning because the fix is minor compared to the part replacement price. Plus, it's a hobby.
Wheel bearings - A few have gone bad, including one of mine. As you are now post-warranty, the "exposure" here would be the same as for any other car.
If my list seems incomplete (and I'm sure it is), perhaps others will add more. But overall it is an extremely competent and reliable vehicle. Little gas goes in, little pollution comes out, and it always works. Change the oil, follow the other maintenance specified, drive cheap and happy.