Please note a full service won’t fix the issue, they will need to replace the damaged gear and then any other gear which directly touches it. This is definitely a serious repair of a grand complication.
On my 3941, I noticed that the hand on the date subdial was well-centered on the dial marker at the end of the month, but that the alignment has gradually deviated over the past two weeks. I used the pusher to adjust the date to test the alignment through...