I see the "detect displays" icon pop up when I hold down the option key, but both the TV and the computer monitor are pitch black when I plug the HDMI cable in, meaning I can't now navigate the cursor to the "detect displays" button. So frustrating! I'm tempted to buy an AppleTV and just stream over AirPlay... But, of course, that's another $100 for a functionality that should come bundled with a $2K computer...
PROBLEM SOLVED!!! (In my case, at least)
My Apple tech support guy came back a day earlier than expected, said to remove a couple of plist files, and it now works perfectly with HDMI, my projector, my external monitor, etc.
I had already removed one of the plist files a few days ago (which in itself hadn't worked), but when I removed the other, it did. I would suggest removing both.
Go to Finder.
In the root directory (MacBookPro or whatever your HD is called), go to Library, go to Preferences, find com.apple.windowserver.plist and put it into Trash
In your own user directory, go to Library (in Finder, click Go menu and hold Option key down to get to Library), go to Preferences, go to ByHost directory, find com.apple.windowserver.OE35739etc,etcxxxxxxxxxxx.plist, and put it into Trash.
You do not have to empty Trash.
The HDMI should be working now, and permanently so.
If it isn't, post it here and I'll let the Apple tech guy know.