I think some of you are trying to over engineer a solution. It's a design flaw that BMW needs to address. By shoving a clip or something in there is only a band-aid. My theory is that the arm is slowly being backed away from the wastegate journal. By shoving something in there, you may cause the issue to worsen/accelerate and possibly back the arm off altogether. There's no performance hit that I can see as any lateral movement at this point wouldn't affect the operation of the gate itself. It's more a nuisance than anything. Until, that is, it fails completely.
Another theory is that any retaining clip that may exist on the other side of that journal (on the inside of the housing) may be getting loose. That said, the same issue applies. These repairs could end up binding the journal and causing some major issues. Try explaining to BMW why your motor blew when your WG wouldn't open up cause you jammed something in there trying to fix something that they should have fixed themselves.
Just my $.02