Ah, I see what's going on - if the "Show Dashboard" keyboard shortcut is left assigned to F12, but the box to the left of that item in the shortcuts list is checked, OmniFocus will pop up a "You can't assign that shortcut" dialog if I try to use F12 for clipping.
However, if I uncheck the box next to the "Show Dashboard" item in System Preferences, OmniFocus will let me assign that shortcut. It doesn't actually work, and I get pretty much the results that folks are describing - shortcut appears in context menus, but there's no box next to the item in the System Preferences list.
Basically, it looks like conflicting shortcuts put something in OmniFocus or 10.6 into a bad state. Even if I choose a different shortcut in OmniFocus now, it doesn't work. Also tried checking the box next to "Show Dashboard", then setting that to something ridiculous like control-option-command-shift-F12 and un-checking the box next to it; I still wasn't able to set OmniFocus' shortcut to anything and get it to work.
In any case, I'll make sure the team knows we can reproduce the problem now - that'll help them a lot. Very sorry for the trouble this is causing!