Also, in Mountain Lion the traditional software update application still exists if you need it. It does not require a login. 

Go to Macintosh HD>System>Library>Core Services and you will see an application called software update. Use that and you can run all updates without issue.

-Logan Cooke
The Warren School

On Aug 9, 2012, at 2:40 PM, Craig Lyndes @ wrote:

go to the update page it says we need to log in using an
iTunes account, and from this point on that iTunes account will be the
only account able to update those apps.