I loosened the 4 screws that attach the cooler to the bracket and the system stopped crashing. These screws are on springs so I'm hoping the heatsink didn't lose contact with the cpu... just relieved some pressure.
CM's documentation is somewhat lacking. It would be nice if they mentioned something about how tight these screws need to be.
As a general rule of thumb, you want to get the heatsink on just tight enough to that its properly, secured, but no more than that. Too much pressure on your motherboard will definitely cause some problems and/or damage.
I'm not sure about the shorting. I don't believe that simply touching the heatsink was causing any type of short, but you might have been applying enough pressure by touching it to cause the motherboard to bend a little, especially when you mentioned that you were able to loosen the heatsink a bit and stop the crashing. Also, I would think that a single short would be enough to put your system out of commission for good instead of causing recurring issues, but don't quote me on that.