The antenna on the FBI car changes from the roof when parked outside Darnell's home to the trunk when parked at the motel.
FBI agents do not use GSA motorpool cars with markings on the door that say United States Government. They use unmarked police vehicles.
When Officer Parker Williams pull away from the suspect's vehicle in the beginning of the episode, you can see the brake lights of the police vehicle down the street when the suspect exits his vehicle before the kidnapping occurs.. surely the officer could've looked in his rear view mirror.
Parker was negligent when he failed to check out the suspicious vehicle in the beginning. All he did was shine his light into the cab. Standard procedure is to check the tag to see if it is stolen and also the passenger area in the event there is a medical problem or a drunk driver that passed out.