The Cd spins so fast, and the twist in the central area so tiny, you would not be able to see it. The biggest flaw in transport technology is that the CD is held only at the inner 2mm or so of the entire disc. So that central area can be off by only a few hundreths of a millimeter, and it will vibrate, especially if the disc is also very slightly off balance.
Like I mentioned, The one disc player that had a solution to this was the Pioneer Elite "Stable Platter" where the entire disc was supported, and the disc placed into the player upside down on a CD sized turntable.
I wonder why no other manufacturers ever used that?
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For some of the problem to be an individual players fault also makes sense, as the typical magnet clamp is pretty flimsy, and might have a manufacturing error that makes it more likely to not seat correctly. If this is the problem, opening the top up and checking the little top puck might help. The usual way it is in there the top clamp is held in a plastic holder, that only loosely/approximately lines up the spinning motor and the upper clamp. You can watch it load with the top off and see how it clamps on some of the vibrating discs. Perhaps all you need to do is push/bend the plastic holder of the top puck down a fraction of a millimeter. (I have done this)