The scenario: You see a public game that you may want to join, but there are some questionable characters in it. The rating and rank systems may give you somewhat of an idea what you can expect, but perhaps the best indicator is your own personal history with the player.
Right now, you can find mutual games via "Game Finder", but that involves a bit of navigation and typing, and by the time you're done, there's a good chance the game will be gone.
I propose adding a button to the Join A Game page next to players' names/ranks/ratings for finding mutual games (games you've played with the player, if any). I'm not sure how hard something like this would be to execute, but if not very, then I think it would be a big help.