At the storage facility Jane hits the side of the car and you see sparks. However when the detectives get out of the car there are no scratches and no damage to the car at all.
In the storage facility scenes, the red and blue lights are flashing on the police car, then they are not flashing before the homeless person is seen, then they are flashing again prior to the traffic stop.
The lie detector segment contained several errors. Suspects never face the machine and watch the results. They do not give an answer beyond yes or no. They are not presented with questions by anyone other than the machine operator.
Maura just had brain surgery but in all the scenes after that surgery, her hair is perfectly intact. It would have been shaved, at least partly, for the surgery and there would be bandages on her head.
The arrest of the husband at the storage units would not hold up in court since there was no cause to stop him. Additionally, the seizure of the murder weapon would be excluded since police are not allowed to search and seize in the manner shown without either consent or a warrant.
Maura says it's hard to get used to being mothered as though she grew up without a mother, but she had a loving adoptive mother which she acknowledged on more than one occasion. Her statement, while warm and fuzzy and serves the purpose of the writer's intent to bring Maura and Hope closer, is nonetheless inconsistent with the story line from previous episodes.
When Clair is arrested, she is placed in the police car with her backpack. Persons under arrest are searched prior to transport and are not allowed to retain personal possessions, especially one large enough to contain a weapon.
Maura notifies her birth mother about her surgery and Jane keeps saying she is her mother, but prior to her discovery, Maura had a close relationship with her adoptive mother and even told Jane that Hope was not her mother, her real mother was her adoptive mother. It is out of character for Maura to ignore her adoptive mother by not telling her about her surgery.