The email Kim receives at around 43 mins does not match the one Dr. Duntsch sent her. Dutsch writes that he is a "stone cold killer". Kim's email reads "stone killer".
In the first opening scene, Dr. Death is scrubbing up right before surgery. He then walks into the surgery suite and touches the patient on the foot with bare hands. Scrubbing in for this surgery would've been pointless at that point.