External monitor has "sun spots"
It could be the monitor, the cable or VRAM/ something else in your Mac going bad.  

Easiest way to test would be to use the monitor on another computer or with another source (like DVI) and see if the problem persists.  Preferably with a different cable to limit things to the monitor.  

If you can borrow a DVI adaptor from a friend, that would be a cheap way to see if DVI would fix it (either by replacing VGA or perhaps the VGA port on the monitor is going bad - it happens).

Finally if the monitor behaves with everything but your Mac, then it could be a hardware problem with your Mac.  Since your Air uses integrated graphics there is no dedicated VRAM - and since there is no problem with the native screen, the more I think about it, the more it sounds like it's probably a problem with the monitor itself.  

Unfortunately there isn't an easy way to tell without doing some testing as suggested by others already.  Good luck!