Apparently Apple doesn’t want you to take a screen capture of your DVD movies. When the DVD Player is running, the standard keyboard shortcut Command-Shift-3 is disabled. I did some googling and eventually found a nice work-around.
Run the terminal, run ‘screencapture -c’ to copy the entire screen to the clipboard. You can even tell screencapture to write directly to a file. The only difficulty I have right now is that I can’t run a movie full-screen and still make the capture. There might be a way to tie it to a shortcut key, but my Apple skills are weak.