"I'm wondering what the principal disadvantages might be?"
No airline would buy it????
I seem to remember Bill Gunston discussed the advantages that Boeing discovered when they designed the B-47 - in addition to the points mentioned by tdracer they found less drag, much safer in case of an engine blowing up, much easier to upgrade to bigger engines later (also see the 737)
It's no coincidence that the Russians went for under wing engines after the Il-62.
jets at the back still have a place on business jets and small commuter aircraft but I can't see anyone designing a medium/large airliner with rear engines again