Does this sound like a shutter button problem ?

Occasional problems with my 5D MKII ... at first a couple months ago the shutter button would stop working and I would have to reboot to get it working properly again. Lately it will occasionally fire twice ... the mirror will flip twice but only one exposure is taken.

Any thoughts ?

There's a computer in there...

If it's not something you can replicate on demand by physically doing something, it could be the button, a circuit board or it may have just gone stupid.

Have you tried removing both batteries (power and time/date) and let it sit for a couple minutes before re-using?

Do you have a grip on it? If so does the problem occur with / without?