Xbox – More Songs for Rock Band 4

There currently is no way to do this after you fail the song when you are tour. You can restart, however, just before failing by hitting start and restart song.

I've been informed a game was ready to start only to find that it needed to download more a few times. It's a little frustrating.

I've never had any issues with corruption or anything like that as a result of playing the game once it finally let me. If the game allows you to play it before the download is 100% complete, that is by design, so it shouldn't be any more likely to corrupt your data then any other time it is operating by design.

That being said, not all development houses are created equal, and sometimes bugs will slip through. So, no one can tell you definitively that this will never happen. You should be fine, though.