[Vincent]

Ok, after posting I pulled the car apart and started bending the steering spring into different shapes. Like I said, the car is old and this has caused the steering spring to go kind of limp over time.
The edges extending from the spring were not completely over the trim nob. I finally bent the spring into a shape so that they would be around the nob giving the wheels the ability to spring back into the neutral position. It's not a perminant fix, though. The car still isn't like new. A new spring should fix the problem.

I used to have the AE86 collector's set (the origional with the red and panda bodies). I gave it to a friend because while cleaning it, I lost the steering spring. He finally found a replacement. He used a calculator that had a spring loaded top (the kind where you hit a button and the top flips off to reveal the crystal screen and then over the back to prop the calculator up).
They can be bought at most office supply stores for cheap.

Hope this helps anyone who has either of these problems.