Thereunto: If you send the autosave file, the other player will have the screen for the start of their turn.
Before I complained about how hotseat works, I actually tried it with a random scenario. On my game, at least, auotsaving happens when the "End Turn" button is pressed, i.e. on your turn, not the next player's turn. If you load the game, you will return to just before you pressed "End Turn". The next player will have to press "End Turn" again without looking to be fair about it.
This is my main complaint. I only mentioned file sizes because greyhuntr said that's why PBEM isn't supported, and I offered some alternatives that don't require their servers. I can think of a number of other alternatives as well, and besides, my email doesn't have file attachment size restrictions that I know of.
As a secondary issue, the only thing you can do on the next player's turn is start it. You can't even exit the game without starting the next player's turn to get to the menu, unless you kill the process, at least as far as I can tell. The password protection would cure accidental entry into other players' turns, at least. It's not a security measure: you still have to trust the other players, but you shouldn't make it almost a requirement that they cheat.