What causes a car to jump in reverse when all forward gears are fine?

I once owned a 1967 Ford Mustang (sure wish I still had it!) with a 289 ci w/2 bbl and factory 3 speed on the floor. I bought it used with 100k miles. It acted fine in forward gears but when I put it in reverse, It "jumped" as long as I was moving. I changed out the clutch and pressure plate twice but it didn't help. Could it have been that the fly wheel needed balancing (by grinding) or something else?

Wrong track. The clutch, pressure plate, flywheel, and transmission input shaft do exactly the same thing, forward or reverse.

I'm thinking that you had a problem with the drive shaft; bad U-joints, maybe, or a differential problem.

Reverse is super low gear. Some cars do jump depends on engne tranny rear gear ratio… I've owned 50 cars over last 60 yrs.about 10% manual tranny cars jumped

Are you planing on fixing a car you no longer own?