The 'cup' where the end of the shift goes into on the tranny...is this cup supposed to be attached the metal piece or can it move freely? I can take mine out with no problems, it's not glued in or anything. Would this cause my car to jump out of reverse?

 

Have you ever accidently missed 5th gear and hit reverse instead, not actually going into reverse but grinded it. I know it sounds unlikely but I managed to do it racing a corvette on the highway years back. After that it feel out of reverse almost all the time unless I happened to engage it just right.