By DVDs do you mean movies or the game discs themselves? Also if it is games then is it specific games that do so?
I had the problem once with one of my 360s.
Try to clear your system cache.
In Xbox Home--System -> Storage -> highlight the device -> Press Y -> Clear System Cache -> then restart your console
That worked for me.
did not work, still giving same error. Every time the xbox restarts it plays the dvd a bit further. after about 6 to 8 restarts it plays the dvd
This is only with movie and music DVD's
When watching movies or playing music, the disc tries to buffer a lot of the info. Since Microsoft OS's use a lot of virtual memory (which is utilizing your storage space as RAM,) check your 4gigs and see how full it is. You may need to delete some of your older files off of it (ie save games you no longer play or games that installed themselves.)
I'm having the same problem with Watch Dogs i think it's because the disk is Dolby Digital correct me if i'm wrong.