This seems to be a somewhat common problem when going from Lion to Mountain Lion and storing contacts in Apple's Cloud.
I've seen the same complaint on two other forums.
But the steps listed in the Apple article above may be overkill.
Referencing the Apple article for file locations, others are saying all that's required is to delete the Address Book folder in the Applications Support folder and then restart the Contacts app. Another person said what worked for him was to trash the the same Address Book folder and the two Prefs files.
If I had this problem, I'd start by deleting only the Address Book folder and see if that works. That's drop dead easy to do and quick.
It's not like you're going to lose anything by trying. Everyone has said their contacts are still intact when going to iCloud.com so it's an access problem. You can confirm that by signing on as a different user and opening the Contacts application (and entering the correct Apple ID info of course).