I have a MacBook Air 13", bought about a month ago, running OS X 10.8.5. The camera is recorded in System Information as:
FaceTime HD Camera: Model ID: Apple Camera VendorID_0x106B ProductID_0x1570 Unique ID: CC2332357XYF9T9CA
The camera worked in Skype very well until last night when I installed the latest upgrade from Apple. After that, the camera will not work in Skype although it works on PhotoBooth and iChat. In the preferences Skype declares that there is no camera. I reboot the system a few times. I unistalled and reinstalled Skype (the latest and some of the earlier versions). I performed SMC and PRAM and I fixed the permissions. I open Photo Booth while Skype was running. Nothing worked.