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.
Character mistake: In the first call to a working structure fire Severide proceeded to head towards the basement from the middle level by walking down stairs but falls through. His first mistake was not checking the stairs with the halligan as any firefighter is taught, to check if they are sturdy. And last but definitely not least no firefighter should ever walk down stairs, especially wooden framed ones if they are on fire.
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.