If I play a Hulu video in a browser on one monitor and then click the "full-screen" button, the video takes over the whole screen. But a glitchy copy of the video also takes over my second screen. But I'm not running my two monitors in mirror mode. I'm using a Radeon HD 4650 graphics chip.
Flash didn't know this, just until recently, so try updating flash and download the latest one. The latest features include fullscreen only on one display.
Check this article.