Watching for 40 years, didn't notice until now - need confirmation
If you watch during the "Puttin On The Ritz" scene, very briefly, on the right hand of the stage you can see Igor playing piano. You have to wait for the camera to pan far right. It is not the focus of the scene, but it is consistent with two other observations:
> Before the number, Inga is by herself in the wings, and Igor is not in sight.
> At the end, Igor turns up in white tie and tails - the prefect costume for an accompanist.
Did I see this correctly?
Well, there it is.