I had a similar issue where the hand was aligned in one consistent section of the subdial but not the other. What you describe is a symptom of gear teeth being damaged. It needs to go in for service to Patek, only option.
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...