How can the colors of a single window be inverted in OS X?
You can use Command ⌘+Option ⌥+Control ⌃+8 to invert the video colours of the whole screen.
There's no way to just invert the colours of a single window.
⌘+⌥+ctrl+8 does the whole screen if that helps.
You could make the window full screen!
In Mountain Lion, the Ctrl+Opt+Cmd+8 shortcut was deactivated. I first had to activate it for it to work via Keyboard Shortcuts in the System Preferences in the Accessibility tab.
Black light software does it, and it does even more.