I’ve occasionally seen issues where Mac App Store downloads failed, with a message saying “The product distribution file could not be verified. It may be damaged or was not signed.” Topher Kessler writing at CNET showed a way you can resolve this issue.
When this download problem occurs, it is generally the result of a corrupted file in a cache folder. If you run this command in Terminal:
a folder will open in the Finder showing a number of cache folders for different applications. Delete the com.apple.appstore folder, then quit and relaunch the App Store application and try the download again.