I recently just bought this Integra. The only thing that I can see that has gone wrong with it is the A/C doesn't work, possibly due to needing to be recharged (because the compressor still comes on), and the speedometer jumps until 70MPH...then it stays still. It has a small patch of rust on the hatchback lid lock, and the front brake rotors are shot.
This is a great car. I would highly recommend it to anyone. The automatic transmission still shifts smooth (even though it would be more fun with the 5-speed). The car is designed really well, being an early '90's car. *If anyone has any idea on how to make the speedometer needle quit jumping, please let me know*
Possibly a loose speedo cable.
The jumping speedo needle is caused by a worn speedo-cable. You will need to replace it before it finally breaks. I have no experience changing a Honda/Acura cable, but it is usually a fairly easy procedure. Good luck.