I just did some minor repair on the flip-out LCD panel on our EX1. Somewhere along the line the mounting screws on ours (where the panel attaches to the pivot) loosened up and a little plastic tab inside the bezel broke. That meant that only one remaining tiny mounting screw was holding it in place until I could get the parts to repair it.
I suspect this happens a LOT because a) the tiny little $75 bezel piece was on back order from Sony for over a month, and b) the replacement screws come with red thread locker on them. When I first discovered the damage to our camera I noticed that the screws did not have any sort of sealant to prevent them from backing out.
If you haven't had this problem, it might still be a good idea to loctite those two screws on the inside edge of the panel. They connect to a metal pivot piece inside the LCD unit, but only after passing through a rather brittle tab on the front bezel. If you want to leave well enough alone, keep an eye on those screws...if they begin to loosen up, put some thread locking compound on them asap.
Major kudos to Steve Cahill for posting his experience on removing and replacing the LCD unit with a video on the Exposure Room website (tinyurl.com/ex1-lcd). I watched it before popping that LCD unit open, and I'm glad I did. It illustrated a couple of little plastic tabs that would make the manufacturers of motorcycle bodywork proud! Since I knew they were there, I knew how I needed to manipulate the rear LCD cover to remove it without breaking anything.