Most of the people watching the operations were either other doctors, medical students or nurses (albeit rarely); family members were usually not allowed in the operating theater. The observers were seated in order of seniority, with the most experienced doctors right next to the action. There is a scene in episode 7 with Dr. William Stewart Halsted (who Thackery is largely based off of) and you get a clear view of who is watching the operation.

Interestingly, quite a few operating scenes had already been filmed when the research team discovered the seating hierarchy. When Steven Soderbergh found out, he reshot all of them!