I had exactly the same problem, which occurred after I had to restore my iMac from my MacBook Pro after the iMac went down and the Time Machine backup failed to work. Fortunately I sync all my documents between the iMac and the MacBook Pro. I think I used Migration Assistant rather than Setup Assistant, which may account for the problem as Migration Assistant is known to cause permissions problems in some cases.
I can confirm that the creation and modification dates of the damaged Applications folder are 24 January 1984 while the Applcations folder on the MacBook Pro has a creation date of 24 April 2012.
Dan's method using Terminal worked with one modification: I needed to enter
sudo mkdir Applications
because I got an error message that I didn't have permission to mkdir Applications. So the correct sequence, for me at least, is
open Terminal
cd /
sudo mv Applications ApplicationsOld [enter password when prompted]
sudo mkdir Applications
sudo mv /ApplicationsOld/* /Applications