Continuity mistake: As the Doctor is being put to sleep, he lies on the operating table which has no pillow for his head. When Salinger uses the defibrillator on the Doctor, he has a blue pillow cushioning his head.
Continuity mistake: When Dr. Holloway asks for the scalpel in the operating room, her gloves are tucked into her surgical gown sleeves, in another shot, the gloves cover the ends of her gown sleeves.
Continuity mistake: When the Doctor wakes up and screams from the shocks, the tube pops out of the mouth tube. In the next shot, when the Doctor falls dead, the tube is reattached to the mouth tube.
Continuity mistake: When Grace is operating on the Doctor, the tray holding the surgical tools is at the end of the operating table, in the next shot (from an aerial view), you can see that the tray is over the Doctor's feet.
Audio problem: As the Doctor is being wheeled through the emergency doors, the emergency room doctors are giving orders about what to do, but none of their lips are moving.
Continuity mistake: When they wheel the Doctor into the emergency ward, Wheeler grabs onto the stretcher and helps pull it, in the next shot it's just Bruce and the other paramedic moving the stretcher.
Chosen answer: I've watched a surgeon perform open-heart surgery, and the radio was on the whole time. Whether music plays is probably up to the head surgeon for the particular operation, but it is certainly allowed.