Since I got my random flipping shutter issue, I have done a lot of Googling to see if other people have had the same issue. During this process, I discovered a few other issues 5D Mark II owners might have and thought it would be a good idea to list them.
While looking at this list, remember that Canon has sold tons of these camera and most of them have no problems. The web is a big ecochamber where one person complaining can generate more noise than a thousand happy customer.
Random flipping shutter
In live view mode (while not recording) the shutter randomly start flipping. I already talked about it here. My camera is still at Canon for repairs. I will write back on this once I receive their incident report.
This issue has been identified by extraordinaire photographer Sam Hassas. The guy is well known for framing the sun with his subjects to create big and nice sun flares. Go look at his stuff and see how cool it is. The downside of this technique is that it seems like he burned the sensor in four spot. Since he has been doing this for a while and probably shot thousand of stills framing the sun, there are probably no reason to panic but it is better to be aware of this.
We are still waiting for details but you can follow the thread here.
While still present after the 1.1.0 firmware update, this issue is not getting a lot of press anymore. I guess people accepted the limitation and moved on to complain about the lack of 24p. You can read about it here.
Some user have reported that they cannot shoot in 24p, citing this as a major issue. We are still waiting for an update from Canon to see if they aknowledge the problem.