They are getting this message. “This Copy of the Install OS X Mountain Lion Application can’t be verified. It may have been corrupted or tampered with during download. Delete this copy of the application, and go to the Purchases page of the Mac App Store to download a new copy”
So far Apple has not come out with instructions on how to fix this. One of my MacBook Pro’s is throwing this error and fails to be able to be upgraded
If you read all of the threads, there seems to be a handful of suggestions out there re-downloading in most cases does not solve the issue. After deleting the 4.3gb file re-downloading, and cleaning out the cache files (another suggestion) the issue remains.
This seems to be isolated by the thread reads are now over 10,000.
Some have tried booting into recovery mode by holding down the option key when powering up and running Disk Utility and running repair disk permissions. One should use some caution here as Disk utility can ruin your day if you press the wrong button.
My specific Mac had a number of issues that the repair disk permissions fixed, but it has not solved my issue of being able to upgrade. Until someone comes up with some more ideas, or Apple publishes a fix I have Mac that will remain on the older operating system.
I will have to admit up to this point I have never had an issue in updating or upgrading a Mac, so now I can equally bash on the Windows and OS X upgrade process as nothing is perfect. This is one weakness of the cloud. If you received a physical disk this type of validation of the download would not be an issue.
Update: After I launched recover mode and ran the disk utility for repair disk permissions, then put the mountain lion upgrade in the trash can and deleted it re-booted and downloaded the upgrade again, I was able to get a good install. Make sure you delete the install file do not over write the previous download.