Well for a start, where is your Jaguar from? As in where was it made? 'Cause the Japanese Jag trem arms just slot in and you have to hope it doesn't fall out, and with the American Vintage ones you push it in 'til it locks, no screw thread on either of 'em. As I understand it though the Mexican "Classic Player" Jags do have a screw-in trem arm, so I'm guessing it's one of them?
I'm not actually sure how the Mexican Jag's tremolo is set up compared to the others, but if it's as similar as I would expect it to be then it sounds to me like the bushing that the arm goes into has been damaged.
