When I got my 27" thunderbolt display, set it up with my 2011 lion MBP was working as it should, my desktop backgrounds was being shared or extended across the displays, when I hit mission control I can see on both displays exactly the same 6 desktop spaces with the pictures I set for their backgrounds, when I draged google chrome or fusion 4 to the external display I was able to make either one full screen just as normal and keep on working on my laptop with other apps(note: my dock & toolbar were on my MBP screen all the time).
Then close the lid on my MBP and went to lunch, when I came back I found that my perfect set up was turned into the nightmare everyone else is living thru the forums all over the internet,the background and mission control backgrounds were the stock lion galaxy looking thing on the external which seems like my MBP desktop wasn't being shared or extended over to the external display any more, and when enable any app to full screen mode on the external display the app jump to the macbook's display and the external"s background tuns gray with a pattern and turns practically unusable compared to the way it should work, you should by able to work on both screen at the same time otherwise would be pointless to have a $999+tax external display functioning this way.
I tried plugging the display with the laptop off and turning it back off, restarting, went thru all the options on displays preferences(which are like 3) and nothing corrected it, so I took it to the Apple store the guy didn't know much more than what I do since his troubleshooting strategy was the same as mine and unsuccessful, the guy "escalated" the issue and made me an appointment, long story short, the guy couldn't figure it out and clammed that the computer was acting as it should, so I was pretty sure that if he connect another MBP to the display it was gonna act the same as mine at the beginning but I was wrong, it was as messed up as mine was. so I decided to call Apple support and the guy was supposedly a display expert and said he knew what I was talking about but I had to purchase a $180 plan for a year or $60 for a week so I can have support over the phone and attempt to fix the problem, later he sent me an email asking for my MBP specs to make some research... provably the same goggling I've been doing the las couple of days.
I'm not really interested in a workaround kinda fix but into knowledgeable way to some how fine tune some settings to get it working as it was when I first plugged in the monitor.