Pick a couple random files that should be in the repo, restore them from a random archive, check the md5sums against the source. If the md5sums don't match (or the file can't be found), something is wrong. I am mainly backing up RAW image files, so they should never change.
The fact that as a customer that is impacted by this, I only found out about it when my backups and automated test restore failed is worrying.
I get that things happen, but not realising that this was going to be a service impacting event does not inspire continued confidence. Sure, this situation probably won't happen again, but what else don't they understand about their infrastructure?