Being on vasopressin (medication to increase and keep blood pressure stable) would disqualify the patient from being able to donate his heart, however at the end of the episode you can see that the last organ to be harvested for transplant is his heart. This would not happen in the real world because the pressers damage and strain the heart.
When Cristina and Meredith are talking to Dr. Burke while he is in the men's restroom, the door swings into the bathroom yet has no handle on the inside of the door to allow for those inside the bathroom to exit. That is the only door for the restroom, so Dr. Burke is trapped when they shut the door.