Factual error: John fires a grenade launcher at a street gang hangout bar front window. Aside from the fact that such a round would hardly have been slowed enough to just roll down the bar, the round is shown complete with cartridge case, which would remain behind in the launcher/gun - it doesn't fly with the round.
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.
Factual error: Samaritan launches a cruise missile at the rooftop of 1133 Avenue of the Americas, where a satellite dish is located. A real US Navy Raytheon SM-6 missile, fired from a surface ship, would shoot down the cruise missile shortly after it was launched and long before it hit NYC.
Continuity mistake: Harold, Shaw and Harold's friend escape from their captors early in the episode. They smash the front driver's side window of a parked car, which they hot wire to drive to the bank where the tapes are stored. When they arrive at the bank, the window is in perfect condition.
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: Mr. Reese and the stockbroker are hiding out with the street people. In the portion of the show entitled "Kill Squad," at about the 2:02 mark, Mr. Reese is building a fire in a steel drum. The paper and wood are nearly overflowing as he continues to prepare the fire. They cut to Mr. Reese spraying lighter fluid onto the pile of wood and paper. However when Mr. Reese throws in the match to ignite the fire, all the debris are way down in the steel drum. As the flames come upward there are no signs of the wood or paper that had been obvious before.
Continuity mistake: While Reese and the witness are hiding in an apartment, the door is opened by the student to dismiss the bad guys with the chain lock on the door. The door is open about 18 inches and yet when the student closes the door the chain lock is normally sized about 4 inches and is still attached.