Hi everyone,
As an art history graduate, I, too, never fully grasped the politics of paid/unpaid museum internships. I agree that often times undergrads are bogged down with administrative duties that their superiors don't want to perform themselves--and while that is a component of virtually any internship, I hate it when it is the basis. The Met internship is highly coveted by most art history students, no doubt, but I know a few former (undergrad) interns whose experience entailed routine admin. tasks; of course this easily can change as a grad student as someone noted earlier here.
For those that are still pursuing their BA, I encourage you all to look into an incredible and substantial internship opportunity at the Smithsonian Institution: Katzenberger Foundation Art History Internship; it pays $5000 for 10 weeks and involves substantial projects in curatorial/research departments of different Smithsonian units. I feel extremely fortunate to have been selected for this internship last summer; my project involved considerable responsibility and I learned a lot!
Cheers!