RAM pack wobble
I believe the root cause of the the dreaded wobble was that Sinclair re-used a RAM pack casing design intended for the ZX80 (which had a flat, vertical rear surface for the pack to butt up against) for the ZX81 (which didn't). See Rick Dickinson's sketch of his intended ZX81 RAM pack in his fascinating (if you're an old Sinclair nerd) Sinclair design archives on Flickr.