Continuity mistake: As he gets B.A. into the doctor's office, the van door is left open. After the interior scene, the van door is closed.
Continuity mistake: As Hannibal talks with "Koochie" his gun is up to mid torso height. After the angle change, he holds it as if he's sighting the lady.
Answer: Several times, Face would pose as a doctor to get Murdock out of the Mental Hospital. How easy would it have been to convince airport officials that he was a doctor taking a sedated patient on board? Or simply tell them, this man is afraid of flying, so he had to be sedated. They could say, "Believe me, you don't want this man to be awake."