I have a 89 RS with automatic transmission. I hear a thump at the rear end when I accelerate hard off the line but if I baby the throttle off the line than there is no thump. Now, that same thump can be heard as the tranny moves from 1st gear to 2nd gear when I'm stomping on that gas pedal.The rear also starts to slide to the right a little bit. I need help to figure out if this is a major problem....Deadbird, you out there to lend a bro a helping hand...(again)

 

Sound like it is time to replace your tranny mount. A broken tranny mount, when you floor it from a stop position, would cause the tranny to "thump" under all that torq. It's an easy fix. Just make sure to replace it with a polyurethane tranny mount.