I recently came across this problem with a small AR project I was working on. Sometimes the webcam would work, but other times the SWF would seem to freeze when the Webcam Flash Player Settings window would come up. I could still “tab” around the settings window but I couldn’t select the “Allow” button to enable my webcam. This was pretty frustrating until I came across this helpful post on stackoverflow:
http://stackoverflow.com/questions/3003724/cant-click-allow-button-in-flash-on-firefox

It seems that it is a bug within the Flash Player Settings that occurs when the window width isn’t a whole pixel, and the CSS for the window is set to margin auto. With a bit of javascript trickery you can make sure that you won’t have this problem again.