I have a '93 Acura Integra with automatic transmission. Ever since I got it some time ago the car has been vibrating a lot when stopped at a light, for example. The vibration is worse when in gear than in neutral, but it's present in both cases and slowly goes away as I drive and get closer to 2k rpm --- car idles close to 1k rpm. Also the problem is worse with a warm engine/transmission than when it is cold, presumably because at higher temperatures it idles at lower rpm.
Now, I noticed recently that the engine mounts were bad, so I replaced them. This only made the problem worse. Someone suggested I try injector cleaning fluid and that seemed to have made a difference, but only until I was done with that one tank of gas.
What could cause this behavior? Should I check the fuel filter or the injection system? Could this be a problem with the transmission and if so, what exactly could be going wrong?
[Edit] At some point when I was doing front axle work (one of the CV joints needed replaced, probably went bad due to the broken mounts) I noticed that there is some decent play in the differential. I understand some play is normal, but I'm also noticing sometimes, after I turn off the engine and release the brake the car will "shift" a few inches forward or backward before settling. Could this be related to the vibration?