I remember going with my mom when she purchased her Corolla new in '96 - and her going with me when I bought mine new 10 years later. I am a full time student and work full time, and thought having a new car meant no mechanical problems. The car worked well for the first two years, but has been falling apart since. The ECU has had to be replaced, but the engine problems persist. Toyota apparently has a "no code, no problem" policy. They apologize a lot that you 'are having problems', but that's the extent of their customer service. My engine feels like it's about to fall out, and they refuse to acknowledge that their solution to the recall on my car has not solved the problems.
I love the cute tail/head lights (I wish my tail-lights worked, but that's just another thing Toyota won't address), the shape of the car, and I like the back-seat cup rests.
The best improvement I can think of for Toyota as a company is to stop making consumers feel as though they are in a business deal with the devil.