Drives have error correction built into them, so that when they hit sections on a disc that are difficult to read, they can work through them usually. You'll notice the drive speed slowing down considerably, sometimes going to an absolute crawl as it attempts to read the data. Of course, the number of read attempts vary with the software being used.
If the errors occur in a manner that cannot be read, then you will get a read failure and the process stops. Some software will allow read errors, then move to the next section, but most do not. ISOBuster, for example, will recover what it can, but with errors in the data, you might just be getting garbage.
When playing video or music in stand alone players, like your DVD or Blu-ray player connected to your TV, the drive within them will often times skip over bad sectors, with just a momentary glitch in the playback, but when copying on the computer, most software will not allow this, and a complete failure in reading a section will shut down the process.