Every single game you make will have to be mirrored on the server-side, otherwise clients will just get hacked instantly, and you'll lose BTC.
Didn't stop to think about that. So, would this be an issue of user security, or flash security? If it is a matter of flash security, there are a number of ways that anti-cheating could be implemented, from, as you said, mirroring each game server-side (I'm assuming this is similar to what facebook games do?), to adding anti-cheat systems to the code for each game itself, i.e. if it were a top-down shooter, before the score is submitted, the game would check number/type of enemies killed vs. shots fired vs. score vs. a random seed per play to make sure that all four correlate before a score is submitted. Just an example. Since we are basically talking minigames, there wouldn't be any local storage that someone could modify to get ahead.
If it is a matter of user security, i.e. users accounts/wallets being hacked, it is my (limited) understanding of the bitcoin system that, sans hacking the actual user account, one would basically have to hack the blockchain faster than the entire bitcoin network.
So, in summary, I suppose that server-side mirroring of games would probably be the easiest way to keep my BTC secure. Looks like I have some googling to do.
Thank you for the advice.