I'm on xbox. I started a new game with a character that will probably die alot on expert. So I'm saving a lot. No quicksave on xbox.

Is there a point where the number on a save can screw you over or glitch out or cause problems?

Not that I am aware of.

A signed short int (smallest integer variable one can get on most systems) caps at 32 767. If it exceeds that it'll roll over to the signage bit and start counting down to -32 767. Once it gets past that there'll be problems. But it probably isn't an short but rather a normal int which caps at 2,147,483,648 and follows the same pattern as a short regarding rollover.

I've got about 20 saves (just officially declared my Redguard an alpha character, so now he has two savegames instead of one). I think I'm safe.