I'm not running squeeze at the moment so I can't give you any help with your exact question, but, there are a few problems that I can see. Gnome3 requires modern graphics drivers to work properly. I don‚Äôt know if squeeze is advanced enough to run these.
I ran Gnome3 on fedora 15 for about a month, this is what I learned. ATI and Nvidia proprietary drivers don‚Äôt do well with Gnome3. The open source drivers are what‚Äôs needed. Unless squeeze contains the most recent version of nouveau and radion drivers and the most recent Xorg, Gnome3 won't perform well. If you have an older video card or the drivers aren't the most recent, Gnome3 will go into a fallback mode, which is just a stripped down version of Gnome2.
One would think you would need to be running testing (wheezy) or Sid to get a functioning Gnome3 at the moment. Unless someone at Debian has created a backport that will update all the needed parts of the graphics system to allow it to run Gnome3 properly.
If there are any squeeze users reading this, please, correct me if I'm wrong.
I'm running Squeeze at the moment. To prevent myself from accidentally destroying my system should [Shift] hit the fan, I will be creating a virtual Squeeze installation in VirtualBox OSE running GNOME 3. I'll post my results ASAP.