Sporadic static-like white dots on external monitor after upgrading to new MacBook Air

After upgrading from a 2011 MacBook Air to a (refurbished) mid-2013 MacBook Air, I'm getting odd behavior with my external Dell 2240M monitor.

Whenever my laptop wakes up, if the monitor is already on (usually asleep), there are this static-like white dots dancing all over the screen. If I cycle the monitor power with the laptop on, they go away.

What causes this? Does the newer MacBook Air have some incompatibility older monitors?

I'd start by suspecting the thunderbolt->DVI adapter you're using (you are using DVI, right?).

Do the dots go away if you just unplug and replug the adapter, or do you actually have to power cycle the unit?