LW attempts to correct the file at the end of the dwnlding process. However, if it was corrupt at its source, there's not much that can be done. If you receive that message it doesn't necessarily mean that it will end up being corrupt. In my experience some yes, some no. It's a personal choice as to whether you should continue. If the files play/behave properly after you've dwnlded them (before burning), then your problem might not be these files but something else. Whenever I receive the error message, 'do you wish to continue', I make a note to always test the file as soon as it has finished dwnlding.
Can you explain exactly what happens in a bit more detail. Are you sure all the mp3's you dwnld are of the same type & that your burner app can handle 'all' these files. There's various types of mp3 that require specific codecs to play. There's also m4a (mp4) format that is frequently showing up in search results nowadays.