According to Apple's technical support article entitled "MacBook Air (Mid 2013): FaceTime HD Camera might not work after OS X 10.8.5 update", Apple is investigating this issue.
In the meantime, a workaround is at http://discussions.apple.com/thread/5306216?tstart=0
See this thread:
1. You need Time Machine
2. Go to folder /Library/CoreMediaIO/Plug-Ins/DAL/
3. Copy AppleCamera.plugin to good place (usb memory stick is the best place).
4. Go to Time machine in date that skype work fine.
5. Change AppleCamera.plugin with file from Time Machine
6. Restart system, Now skype need to work with camera.