Doctors and nurses frequently wear their stethoscopes backwards - with the binaural pointed toward the back of the head rather than the face - while listening to heart or lung sounds. In reality, this would not allow the listener to hear ANYTHING, as sound would be transmitted into the skin at the back of the outer ear rather than down the ear canal.
The illuminated letters of Exit signs seen in the hospital are green in color. Both red and green colors are legal, but individual states enact the building code laws which specify what color sign can be used. Chicago requires that all exit signs be red in letter color. The interior hospital scenes are filmed in LA.
Incorrectly regarded as goofs
None of the doctors or nurses performs CPR correctly, but if done with straight arms and enough force to make a difference, it can (and often does) break the patient's ribs. Obviously it's better to go without a factually accurate portrayal of the procedure than to injure the actors in the name of realism.