I mac Flickering Screen Issue

Having recently went through the process of updating a handful of Macs to the latest versions of Mac OS X as part of a gifting tech support campaign, several Macs developed an odd flickering display problem that was only visible when an external monitor was connected to the Mac. On an 11″ MacBook Air, the screen flickers with any DVI or VGA display hooked up with the standard Min-iDisplayPort adapter, and displays only a white-black noise screen, like an ancient TV without an antenna. Meanwhile on a newer MacBook Pro, the problem exhibited as external display flickering with anything from DVI connections to HDMI, and with different brand monitors, but the screen would display properly just with a persistent randomized flicker. The video below demonstrates the MacBook Air flickering on and off with a noisy picture: