Dr. Kildare and Nurse Lamont administer insulin shock therapy to the unidentified patient. It was presented as controversial, unfamiliar, and experimental, but had been used in the UK and the US for several years prior to the movie's release. It also is a longer process over a period of weeks, rather than the single five hour procedure shown.
Immediately after surgery, several of the doctors take their masks off; this would not happen until they left the surgical room. In the 1930's it was commonplace to remove surgical masks when not in close proximity to the patient.
The doctors removed their masks because the patient died.