If the disc is defective, there's little way around that. Some drives might have better luck than others with a bad disc, but you're generally out of luck. Flippers by their very nature don't mean they can't be copied. In fact, the flippers in my collection are, predominantly, fine. However, check reviews on Amazon.com or other posts on this board about flippers to see how low quality they are. Resulting in unplayable discs, discs that get scratched in the mail, etc.
Going by Blaze's suggestion, you could try another program, just in case, but you're likely going to get the same result. If the disc is not protected with structural protection, which AnyDVD will tell you if it has it or not (Unless the unreadable area of the disc causes a false positive with AnyDVD for structural protection. I have seen that happen before.), you can use the free program DVDShrink freely found on the web. DVDShrink can decrypt discs with standard CSS or no protection on them, but not structurally protected discs. (If AnyDVD is running, DVDShrink can decrypt structurally protected discs, but you should NEVER decrypt those to ISO. Only decrypt to VIDEO_TS files.) If DVDShrink doesn't work, then you can pretty much guarantee it's a defective disc and you won't get anywhere with that drive, and, most likely, get nowhere anywhere else with any other drive.