Continuity mistake: Opening sequence, they are called to Kinzie and Dearborn. They instead show up at Franklin and Erie. After a short run down an alley, they call in their location as 3233 S. Princeton (more than three miles south of where they were, and nowhere near the Loop). (00:01:34 - 00:02:50)
A Night Owl - S3-E14
Continuity mistake: When the woman came into the precinct and showed Erin and Voight her daughter was taken on her phone, she dropped her hand after Erin took it. The very next shot from the reverse still shows her holding the phone as does Erin.
Factual error: Kevin sleeps overnight at woman's apartment. He doesn't share that he's a cop. The next morning in his unmarked police vehicle he uses his handheld radio that was appeared to be stored in the console and shows up on a violent scene with his weapon. It's obvious that Kevin used his official vehicle for personal reasons, and stored his radio and weapon in the vehicle unprotected overnight, which every police officer knows is wrong and a violation. (00:03:53 - 00:04:29)