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.
Download and install the OS X Mountain Lion 10.8.5 Supplemental Update:
- Resolves an issue that may prevent certain applications from using the FaceTime HD camera on mid-2013 MacBook Air systems ..."