Apologies Are Dangerous - S3-E4
Continuity mistake: When driving to their first call that shift (guy stuck between cars), Truck 81 is seen arriving at the scene while it should be still being repaired. When they arrive back at the firehouse, the truck they drive carries the number of the exchange truck they've got (E-..).
Continuity mistake: Brett enters the abandoned factory twice when she is searching for the missing girl.
Revealing mistake: In the scene on the roof when Severide is removing the helicopter door with a spreader, there is no hydraulic pump or hoses attached, just the bare tool. When he sits the tool down you see this. So the spreader would not be working at all.