Galaxy Nexus screen flashes and brightness issues on various button taps and screens
I just had this happen to me. Seeing your answer, Moskie, I carefully removed the apps one at a time from the application switcher by sliding them to the right, testing between each one. For me, pressing home from the web browser caused my screen to do a slow flaah, opening the apps menu made it go bright and stay bright.

The app that caused the trouble? Camera.