You can only verify the data on a disk if you have a reference, valid disk, or preferably, the original disc image used to create the disk. This is why it's preferred at burn-time to use the burning tool's built-in validation after burning (because some CD/DVD media do have intrinsic defects).
Unless you have the original disc image, or the checksums of the files were generated and stored with the files on the disc, it would be impossible to validate the integrity of the data (and think about it, if you don't know what those 0's and 1's should be, how could you?)
One thing that you can test for is physically corrupted media which presents read errors to the actual CD/DVD drive. For that, you can use a disc imaging tool which supports error checking. However, note that this will only validate the integrity of the disc itself, and not the contents of the files.
In terms of software, you might want to look at the Nero CD-DVD Tool (free) or Opti Drive Control (free 30 day trial), but there are several other tools which can do this. Should you try the Nero tool, this article outlines the process using the Nero CD-DVD Speed tool (see the section titled Test #3 - Surface Scan Test). Finally, note that many programs to rip CD/DVDs to the hard drive will also check for read errors.