Continuity mistake: When Jeff Clarke comes by the firehouse, Hermann wants to hug him but Clarke says "I don't really like people touching me." But throughout season 2 Clarke has hugged other fellow firefigthers (Cruz among others) with no problem.
Continuity mistake: Shay is in the restroom at the firehouse after she returns from the horrible incident on their emergency call. She notices blood and human remains on her belt which she frantically rips off to clean the belt and her hands. In the next cut, while still at the sink washing her hands, the belt is back on.
Suggested correction: She never took the belt off.
Continuity mistake: No snow in all exterior scenes except for when Chief Bowden pays a return visit to have dinner with the female resident of the building which was a fire scene early in the episode. He gets out of his car and walks to the building with several inches of snow on the ground. The immediate next scene of Shay (supposedly the same time) has spotlessly clean streets.