If the HDD still has a bad block, most copy tools that try to burn a DVD will fail when they hit the bad block. Reallocated sectors do not matter, those are bad blocks that have been replaced with good blocks from a spares list. Thus, they are "good" and can be used for read or write.
Some disk cloning tools will flag a bad block and allow you to skip it, which of course causes that file to be corrupted. Big danger is if the bad block is in the directory structure, then you corrupt a lot of files all at once.