I reinstalled all of my apps after a clean install of Leopard last night. I figured that I should run a repair permissions to be on the safe side. Well, I walk away and come back half an hour later expecting it to be finished but it was stuck hanging on the same screen you posted...
That leaves us waiting for Apple to come up with a fix shortly.
I upgraded my Mac Mini (1st generation), and I get to the login screen in Leopard, but if I select a user, the finder title bar pops up, and then I get the spinning beach ball of death.
If I boot from the install DVD, and choose Disk Repair from the utility menu, the "Repair Disk" option finds nothing to fix. However, the "Permission Repair" option loops forever, where forever means "more than 4 hours so far", which seems like a long time for an 80 gig disk...
I'm thinking that it's unlikely to complete the process, but I'm willing to let it run the rest of the day and see what happens...
It takes longer in Leopard than it did in Tiger, but it did finish on my iMac after 10 minutes or so. There very few reported errors after installing all of my apps, and no problems with system per se.
According to the OP "forever" but that's kind of a childish description (sorry if that offends but it is).
I've noticed repair permissions does sit for a while but eventually finishes. It's not like copying and pasting a 1k file from one place to another it'll take a while.
I've also noticed that after the "remote desktop" update for leopard the repair permissions take even longer and often reported that something to do with remote desktop client, even reports an error (but repairs permissions anyway).
Run repair permissions, let it sit, walk away, get a drink, use the bathroom, go see the sun and it should finish. If not then you really DO have a problem.
I have "force quit" the disk utility and rebooted etc because I was thinking the same thing "man this is taking a while" but if I let it sit it will finish.