There was one continuity issue that nagged at me. When we first learned about the Men of Letters bunker, we were told it was warded against any known evil. It is why it is supposed to be such a safe place.
With those wards in place, how could the Winchesters bring the King of Hell into the bunker? It should have been impossible.
They had recordings of the actual Men of Letters bringing demons into the bunker, and that entire room was designed for such things.
I believe the wards are more about keeping the location secret more than anything else (hence the blindfold and earphones they put Crowley in). Sort of like the wards etched onto the Winchesters' bones keep angels or demons from being able to find them. But if they're invited in/brought in/send out a signal/whatever, the wards are pretty useless. Maybe a bit of the whole legendary "can't enter unless invited, but the invitation can be revoked" schtick from vampire legends thrown in for good measure.
That and/or it just completely nullifies any powers they try to use within the bunker.