A situation that is hopelessly fucked up. The worst of three stages of goat-ness. First is the Goat Rope, defined else where.
Then there is the utilitraian Goat Fuck. This normally requires a serious amount of work to unfuck.
Lastly, there is the Goat Rodeo. The worst of the three, it is beyond even profanity. It describes a situation that involves many individuals screw ups, and implies that the fuck up is already well underway, meaning that there is no hope in stopping the mess. Usually said with a defeated tone:
Ready to go to this Goat Rodeo? Its gonna be terrible.