When Laverne was pronounced brain dead, she was taken off the respirator but she stayed alive and breathing for at least an hour. If a patient was truly brain dead, they would have brain stem failure, which would make a respirator or bypass machine necessary to keep the patient breathing.
Laverne has a tracheostomy cannula in her mouth instead of the normal intubation tubing. Further into the episode when Dr. Kelso was in the room, Laverne no longer has the cannula in her mouth. The cannula cannot physically reach far enough to allow air directly into the lungs and can only be used through the trachea.
When Carla is sitting with Laverne's "ghost" in the cafeteria, Elliot sits next to Laverne and her arm moves Laverne's sleeve.
When Turk falls off of the back of JD's scooter while playing "mailbox baseball", the camera pans down showing Turk lying on the ground, but you can see his face which is clearly a stunt man and not Turk.
Laverne tells Carla that she slept with Dr. Kelso before she got married. Being a devout Christian and making comments in the past to others, this wouldn't have happened.