I've been reading all morning and this is what I think I now know:
Photoshop will use discrete monitor profiles to properly display images on either monitor of a calibrated and profiled dual monitor setup.
Lightroom (and, apparently, Bridge) use only the profile associated with the primary display and so the images displayed on the secondary monitor are not properly color managed.
I hope I'm incorrect about that last point and that LR 4 behaves the same as Photoshop with regard to dual monitors and color profiles. Anyone care to enlighten me on this?