Good call on Great Ambition. I wouldn't hesitate to call it the most broken action, although Gathering Forces is pretty close. The major difference is in the price. Ambition at only 50 gold is very easily accessible in the early portion of a game, so much so that it becomes a scramble to see who can acquire the most. Example: In a 4-player game, the player who nabs 2 of the 5 copies is very likely ahead. Same with 3 as opposed to 2 in a 2-player match. Pretty degenerate, really.
The single most broken card, though? It's already been mentioned, and I'm surprised that Hero_guy doesn't agree, and that, in my opinion, is the Gatling Gun. An acquisition of Gatling Gun not only has a high potential of "winning a game by itself," but it's also very good at completely changing a strategy on the fly, and for good reason: it's just THAT insane.
Example scenario: I'm playing a 1v1 game vs. a friend using Premiere set Jill (explosives, etc.). He's playing Premiere set Barry. Our pool is pretty balanced with solid actions, Flashbangs, the Broken Butterfly... everything either of us could want. My first explore nets me the Gatling Gun and I toss the explosives plan out the window immediately, only occasionally nabbing a Flash for extra explores, and proceed to rip the mansion a new one with this weapon that, according to one person, "isn't broken."
That, in a nutshell, is a broken weapon. When your character's strengths and abilities no longer matter and you can simply win on the back of a card that has no balance to it whatsoever. I'm not sure if you just haven't played with the weapon enough, but feel free to play 1 or 2 or 50 more games with it. Maybe then you'll understand how insane it is.
Sorry for the long rant, but man, that weapon makes my blood boil. I just really wished everyone realized the disgust that card brings to the table. There's a reason why I've removed it from all of my mansions accordingly, you know?