Get the latest 5D Mark III firmware here. It gives you now full, uncompressed HDMI output, fixes some speedlite issues with the focus assist light and a couple of minor things.
Add-on: I tested the new firmware and apart from the better HDMI output, which still has its flaws, the most issues dont affect me that much. But what will affect more people is the fact that now the 5D Mark III doesnt recognize 3rd party batteries anymore. You can still use them, but the battery level-meter will not work properly. So, if you dont REALLY need any of the improvements like better AF-Assist-Light behavior when using a speedlight or some lens issues, then i recommend to stick rather with the older firmware and wait until the public outcry will solve the issue with the "Canon only" batteries when the next update is coming.