I accidentally hit the goal without getting the coin and I can't figure out how to go back a level.
Once you reached a flag you can’t go back to the level you just finished, unless you go back to the menu and start a new game. But no worries, you can finish the game without collecting all the gems, they’re just bonuses. There might be something like a secret level unlocking if you collect them all but it’s a secret so I shouldn’t tell you about it… ;)
I was afraid of that. Maybe put some kind of a warning so people don't start playing the game, get several levels in, and then find out the hard way. Or add a level menu or a way to move back and forward through levels you've beaten so people can get all the extras without having to worry about having to start the whole game over.