We run our SMARTBoards in school from Mac minis, some of which are old enough to have DVD drives and so which make use of Super Drives. Anyway, since Mavericks there has been an issue where the DVD player will crash upon loading. Annoying.
After trying out things like resetting the PRAM and the SMC, it turned out that the issue was due to the second display. The machines have two displays: a monitor connected via DVI and a projector via VGA (which are mirrored). I tried changing which screen the display was optimised for (in System Preferences > Displays) and this seemed to do the trick. Yay.
Primary ICT 
Good info. We had the same problems over here when we turned on mirroring with DVD player open. In some cases you can delete ~/LIbrary/Preferences/com.apple.DVDPlayer.plist
That fixed it for some. Another person fixed it by Unchecking Mission Control “Displays Have separate Spaces” – those seemed to fix the user account level issues with the crash. As an alternative you can just drop your DVD disk onto VLC and Mirror away.