When Maggie is first shown at her family reunion, she is wearing a sleeveless blue striped outfit. A few minutes later, just as her sister is leaving, Maggie is wearing a family-reunion T-shirt. When she is next shown at the hospital with her sister, she is wearing the blue striped outfit again. Even if Maggie had put on the reunion T-shirt after getting to the picnic, it's unlikely she would have taken the time to take the shirt off before getting to the hospital, as she was involved in a medical emergency.
When the new surgical resident is scrubbing next to Dr Rhodes, she brushes against her mask on at least two occasions. This is breaking asepsis and she should have re-scrubbed. Everyone scrubs without wearing their mask, for clarity of dialogue, but again this is poor aseptic technique.
It seems the heart surgery was during the day. By the time Latham left the hospital it was evening; Shabbat was over so no need for someone to push rhe elevator button.
Measles is highly contagious. Everyone in the room with the patient should have been masked, gowned, and gloved.