I see your logic regarding the music being composed after the filming. That would be the obvious answer; but original hand-written Brahm's manuscripts (or even copies) weren't just lying around in that state, of course. It still had to be produced by the props department. I just found it curious that they chose to copy an existing waltz already known by Brahms. Perhaps it wasn't their fault at all -- maybe they were asked to create a manuscript simply to lay on the piano while Spock played (which they did) -- and the director (not knowing) chose to include a screen shot of it by accident? Thus: creating this post all these years later ... Thanks, Maurice!