Took the car to a local indy shop that's worked on it with the two previous owners. I wanted them to run the codes on the CEL, and see what was going on. This is what they told me:

P1775 trans system mil fault
P0300 random misfire
P1313 catalyst damage
P0727 engine speed circuit no start - possible crank sensor

Other than the CEL being on, the car seems to run just fine. They said the last three codes (non-trans related ones) could be interrelated, and in order for them to chase them down, I'd have to drop the car off and leave it with them for the day.

Now I don't mind paying this shop a few hundred dollars for them to fix whatever's throwing the codes, but I'd like to have a better idea of what's in store. They said it could be something as simple as a vacuum leak, or maybe not. The only way to know for sure is to leave the car with them and they'll look into it. The car only has 92K miles, but being 16 years old, I would expect some things would be wearing out based on time.

Anyway, if anyone has more details on these codes, or what to expect if they look into it, I'd appreciate it.