The wobble you reference is a clear sign that the screws are loose. That was the sign on each of my lenses that had this issue. If you use a lens on a tripod you notice easily, but if you only handhold the lens, it's more difficult to notice a problem. If you get to the point of a wobble, you have more than just a single screw loose - all four are loose to varying degrees. It may take just a half twist or they may be much looser.
It's quite possible that a loose screw or plate that is ignored could lead to damaging the threads. Also be aware that manually tightening the screws to could break the adhesion provided by any thread locker that might have been used, so you need to use Blue or Purple Loctite to properly tighten the screws.
This kind of thing is a nuisance, but easily handled. I also keep a set of JIS screwdrivers, a set of Allen Wrenches, and a small tube of Blue Loctite in my camera bag. My "spares and repairs kit" also includes extra lens and body caps, sensor swabs, a rocket blower, and Zeiss lens wipes - all in a small ZipLock bag.