I'm running a Mid 2011 Mac Mini with these specs:
2.7 GHz i7
8 GB 1333 RAM
AMD Radeon HD 6630M 256MB
10.8.2

My main issue is when I'm playing a game, my second monitor start flashing uncontrollably. I play fullscreen on my main monitor and have my Dock on my second monitor, and during the game it's constantly flashing during the game. Also, if I move anything on the second screen while the game is in progress (this includes the loading screen) that flashes as well. What I mean is if I had a website open on my second monitor and I scrolled up/down on it while in the game, the screen would flash between the pre- and post-scroll.

Second, I was wondering if there's any way to keep the mouse within the game window during a game? When I have the screen unlocked I'm able to move my mouse to the edges to move my view just fine, but when it comes to doing lots of clicking, like kiting or in a teamfight, my mouse often goes outside of the game window and then clicks on something on my second screen and then the flashing begins.

Do you have the game in borderless or windowed? I have mine in fullscreen, and the mouse is locked to the monitor in which the game is displayed. I can't say about the flashing screen as I haven't had this issue.

It's in fullscreen. The mouse is locked for the most part, it's just that when I'm doing a lot of clicking and moving (ie: kiting) my cursor can briefly go onto my second screen. Since I'm doing a lot of right clicking, I end up creating new folders and stuff on my desktop (in my last game I created a new untitled folder, created a shortcut to the same folder and created a second untitled folder).

In combination with the rapid flashing it gets incredibly annoying to deal with, and I'm not sure how to fix it. Alt-Tabbing makes whatever was currently flashing stop flashing, but when I go back into the game things start flashing again.

I have the exact same problem. My mouse does stay in focus, but the apps on the my secondary screen, which is in this case the laptop screen start flickering like crazy, whether it be spotify, safari, or anything else really.

I have a 15" MBP Late 2011 4gb Ram with a Radeon 6750M Graphics Card.

I have the same problem on my second monitor, when I'm playing i'm able to click on the second monitor rather easily during the game alt tabbing me to the desktop. Makes it hard to win games.

Enabling software mouse fixes this. Though software mouse is a beast of its own.