There are two ways to solve this. One that's simple, and one that takes a little more effort. In the end, it depends if you want DVD Player to remember where you've left off on the discs you've viewed.
Go to: User Library > Application Support > DVD Player.
Inside the DVD Player folder is one called Settings.
If you don't care whether or not DVD Player remembers where you left off on the discs you've viewed, trash the Settings folder.
If you do care, then you need to be a bit more surgical. First, go to File > Get Disc Info in DVD Player while you've got the disc that won't play properly in the drive. Look at where it says 'Settings File' at the bottom of the window. Though there's a 'Reveal' button, it's always grayed out on my system -- but it may work for you. If not, jot down the settings file name, quit DVD Player, then delete the corresponding file from the Settings folder.
Either way, whether you've deleted a single settings file or the entire settings folder, your disc should once again be playable.