Nero CD/DVD Speed is a program designed to test burned disks. In a general sort of way you can see the quality of the burn, at least in the way the data is played back off the disk. It contains several tests....the transfer rate test works with most any drive. The quality scans work with specific types of drives, including older BenQ, some Samsungs, Plextor and Lite-on drives, among a few others.
If you want to copy dvds that you own, then you can use DVDFab HD Decrypter to copy the disk to the hard drive, then use DVDShrink to reduce the size of the movie to fit onto a blank dvd. You can then burn using Nero.
DVDFab HD Decrypter is free (and will continue to work even after the trial for the main section of DVDFab expires) http://www.dvdfab.com/free.htm
DVDShrink is also free. http://www.cdfreaks.com/software/Copy-DVD-Movie-Software/DVDshrink/DVDShrink.html You should read the guides for using it here in our Copy Movie forum, or at other sites like www.mrbass.org