For your info (and anyone else with this problem), I have a relatively new iMac - 1 month old - tried DVD player for the first time yesterday morning and it wouldn't work whenever there was a disc in the drive. I phoned Apple UK support and after a few minor tweaks and reboots was taken through the steps to do a complete re-install of OS X Mountain Lion. What the chap didn't tell me before I started was that Apple expect everyone to have super-fast broadband. Well, here in rural Britain that's a (very) long shot! I only get 1mb download speed on a very good day with the wind in the right direction. My machine started downloading updates at 1000 yesterday and didn't finish until 2230 yesterday..... then I had to 'Check for updates...' which took another 3 hours!!! Guess what.....?? DVD player still didn't work!
Judging from the numerous posts here and on related links - this is a MAJOR DVD player bug. I can't now book another call to Apple Support until this afternoon (but they are going hear what I have to say in their 'How did your support call go....?' e-mail!) so I've tried a fix from another postee which has certainly worked for me. So if you have this problem, it may be worth a go:-
1. Go to this link http://www.tonymacx86.com/attachments/mountain-lion-desktop-support/28161d134506 5241-solved-valid-dvd-drive-could-not-found-70012-mountain-lion-dvdplayback.fra m ework.zip and it will download the previous Framework version (5.5.0) of DVD Player (current Framework version is 5.6.1).
2. In Finder, open the following folders: Macintosh HD ---> System ---> Library ---> Frameworks. Locate the folder 'DVDPlayback.framework' and rename it 'old DVDPlayback.framework' (just so you still have the original if you need it). You will need the Administrator password for this operation.
3. Take the downloaded folder (which should also be called 'DVDPlayback.framework' and drop it in the 'Frameworks folder' alongside the original folder you have just renamed.
4. Now try running DVD Player again and it should work. Once running, you should be able to go to 'About DVD Player...' on the File menu and it will show you the app version number (which shouldn't have changed) and the framework version number.
My main gripe here is that Apple Support MUST know that the latest DVD Player has a problem under Mountain Lion but they're not admitting it. So come on Apple - I expect this kind of deceit from Microsoft but I'm really disappointed that you're just as bad. This is why I've moved from PC to Mac. If you have a bug, just tell people to bear with you while you fix it - don't send us all round the houses!
Good Luck!