A few more bugs I have found:
All new major fights (lavos spawn, lab 64 and the dinossaur) can be run away from. Upon running away, you get the reward as if you won the fight. The Medina 1999AD fights may have the same issue, I haven't checked those.
After fighting the dinossaur, you can get stuck in it and must reset to progress.
Other than that, I must say I'm impressed with the amount of stuff to do in 1999. I will definitely post a review as soon as I finish (just need to find out if I'll ever be able to ride the flying dinossaur in 1999, and then I'm off to beat Lavos).