Quite annoyingly after the computer goes to sleep and wakes up again, some applications have trouble recognising the built-in camera. Up until now I resorted to rebooting the Air, which is not that a big deal when you have an SSD, but still I wished I didn't have to. Turns out there is an easier solution: an application called VDCAssistant is reserving the camera in these cases, which is safe to be killed either from the Activity Monitor or by issuing:

sudo killall VDCAssistant