In Extremis - S2-E20
Continuity mistake: In episode S01E01, it is established Fusco is a detective in the Vice Squad, and later Finch arranges a transfer to Homicide to keep an eye on Carter soon after he accepts the offer for redemption. In this episode during a flashback Fusco is a homicide cop. (00:18:25)
Continuity mistake: Reese orders the cab driver to smash through a car blocking their escape which causes considerable damage to the front driver's side of the car. This damage is shown in one of those computerized captured pictures this show uses throughout each episode. Then in the next scene, when the cabbie is standing alongside his now parked cab, the front driver's side is now perfect, but when he walks around the car to talk to Reese, the passenger side is damaged. The passenger side had been untouched in the crash.
One Percent - S2-E14
Continuity mistake: Immediately before Logan Pierce, who Reese is protecting, jumps into his fancy sports car to pull away from valet parking, the street is packed with traffic, has multiple lanes, a divider. Yet, in the next scene he is pulling out and accelerating the car in an empty single lane street with parked cars and trucks.
Continuity mistake: When Reese is following the Drakes into their office building and speaking to Finch via the earpiece, it is dark and raining; but when the shots change to Finch driving during the same conversation, it is not raining and is much brighter outside.