The media test does not apply to the DVD, because there is no checksum on the disc. That's why the test only takes a short time, as soon as it sees the checksum is not there, it exits.
What exactly is the error message you see when trying to add applications? does this happen whatever you try to add? If it only happens with the odd packages, I'd suspect an error on the disc. If you have trouble installing anything, a fault disc is unlikely, or you wouldn't have been able to install in the first place.
Some more details would help, like the error messages. Also, do you have more than one CD or DVD drive on this computer?
"Insanity: doing the same thing over and over again and expecting different results." (Albert Einstein)