Kiwitim,
I guess I should update my final resolution to this post. I took my air and display to Apple store and worked with staff there at least seven times, because this problem annoys me so much(camera, usb, and sound) and I had no luck fixing it on the fly using other methods. So here is what happened.
As a first round of diagnosis, staff in apple store claims that the port on mac air is broken. It took them a week to have the logic board replaced. Unfortunately, problem remains.
Then they told me this problem is escalated to the engineering level and some engineer from Apple will call me and try to help me to address this issue. Obviously, they acknowledge this as a common defect. I gave it another 3 weeks, got no call.
Resubmitted the request for escalation, no call for another week. Finally, the manager from Apple store decided to swop my mac air with a brand new mac pro, because they claim there is a known issue with mac air working with this display. That is how they deal with this kind of recurring issues with customer, I guess.
After swopping, my display still refuses to work. So they bring a new set of thunderbolt display, and tested with the new mac pro, and it works! So they swopped the display again. For this matter, I'm very pleased with apple's customer service. It does took me a lot of time.
Anyways, my new pro and new display is working so far, just like my air with old display when I first got them. But I don't know if this problem is going to come back... Fortunately, all my devices were still under warranty at that time.
So my suggestion really is to go to apple store and keep bugging them until they have this problem resolved for you, if the problem is replicable. I still think there is a common issue with mac air and this display. As they claimed, switching to pro might help (God knows for how long). In my case, my old display was also defective at that moment because it doesn't work even with a new pro.