http://iscoresports.com/

Halfway through entering a game. Scorekeeper on paper listed home and visitor wrong. I didn't verify until 4th inning. Is there any way to swap home and visitor after game has started?

There is not a way to swap after the game has started. Prior to game start time, when the lineups pop up, you can tap Options -> Swap Teams, but once you have scored some innings, you can not make this swap.

I figured as much. Is there a reason this isn't an option?

Because the current state of the game is stored with every event in the system. This includes whether it is the top or bottom of the inning. We will add it as a request for future enhancement, but it is not something that comes up very often.