How to increase stability of weakest link in camera/plate/head/tripod ?

[astroNikon]

With just the plate on the bottom of the camera, is there any jiggle there (maybe the screw head doesn't have a flat flush inset) ?

 

[Gavjenks]

Most camera plates have some sort of rubber surface on top of them...but it's certainly possible for that rubber to wear out or to come off. If it wasn't there, then I'd imagine it could cause an issue. Hence the flat rubber washer.

I'm also wondering how much torque you're applying to the screw....maybe not enough.

Since this is happening on more than one camera, maybe the problem is just with the plate/screw. Have you tried another plate?

Unless the rubberized surface sticks out beyond the edge of the screw threads, then it won't provide any tension form being compressed, and thus won't have the same thread-locking effect as an additional rubber washer.