With empty (fired cases) in all chambers, cycle the revolver as though it were being fired, but hold the trigger down at the end of the stroke. At that point, the cylinder should be locked up at its best and exhibit little or no movement.
At that point, movement = wear and/or problems and needs to be addressed, probably with a new part or two. Just a WAG, but I imagine the cylinder stop is to blame, assuming the notches on the cylinder are not completely wallowed out.
Equally important is the way a revolver comes up to lock before the hammer falls. If you pull the trigger very slowly, you should hear two distinct clicks as the hand and cylinder stop move into place. Finally, you can use a bore-diameter range rod to check bore-to-chamber alignment for each chamber, and know that all is as it should be!
Froggie