Plot hole: The FBI is looking for a "very tall" guy who has been identified as such by various witnesses and by their own expert due to the entry angle of a fatal bullet wound - 6'5" at least. They send Elena into a bar near the end of the show to meet the Albanian perp who when he arrives is barely average height.
Undisclosed - S2-E7
Continuity mistake: Agents follow the suspect after the shooting in an apartment. They chase him upstairs and out of the door but are still at street level.
Factual error: The Saturn in the show is an Ion which stopped production in March of 2007. Therefore, it couldn't be a silver 2009 Saturn they were looking for.
God Complex - S5-E23
Continuity mistake: The chase scene when Maggie, Tiff, and A are chasing the suspect is a total mess. Maggie radios in to say "he ran down the subway", but he doesn't and they pursue him in the streets. Almost immediately, the suspect hijacks a car three blocks away. They locate him in Queens, but now it's night and raining. However, when the chase began, it was bright daylight and clear. Maggie chases him into a crypt, and in the last scene, daylight is shining through a window.
Character mistake: OA says that Vickers went to Erasmus University Amsterdam, but the Erasmus University is in Rotterdam not Amsterdam. (00:07:03)

Visible crew/equipment: When the team of Special Agents are at the auto shop in Red Hook, just as Scola says, "Ethan Chen, you're under arrest," there's a visible pink nylon T-marker on the sidewalk. (00:20:15)

Prodigal Son - S5-E3
Visible crew/equipment: After Agent Hobbs reads the text that Zack sent to Clayton, Jubal tells ADIC Reynolds they need to evacuate Chapman, and in the next shot facing Reynolds there's an orange T-mark taped to the floor behind him. (00:19:35)
Continuity mistake: Early in the show when Vince is driving to the hospital after he is wounded by gunfire, he gets out of the car twice.
Continuity mistake: Early in the episode in the aftermath of the shooting in the pawn shop in which the two glass doors have been shattered and all glass has fallen, there are scenes with large sections of broken glass in the doors.
Continuity mistake: The chase scene toward the end of the episode is a mess. Toward the end of the episode, Scola runs through a door twice while chasing the suspect and, just a few scenes later, Tiff, while chasing another suspect approaches another door twice before she enters.
Continuity mistake: Toward the end of the show Scola and the brother of the principle terrorist emerge from the building containing the now disabled bomb. The brother and Scola exchange a few words and the brother walks away. After a very quick camera change the next shot shows the brother far away from Scola, much too far for him to have walked given the shortcut away.
Continuity mistake: Nick drags Nathan out from the silo where they are hiding twice.
Continuity mistake: The scenes of OA and Maggie chasing McGowan are a mess. The distances between the agents and the perp vary greatly from moment to moment and OA is going over the same fence twice.
Continuity mistake: The two FBI agents are searching for the wounded perp and track him to a veterinarian's-the woman working in the office is ordered to the ground and lays down in front of office chairs very close to large animal cages by her head. In the next scene when she is ordered to her feet, the cages are nowhere near her.
Liar's Poker - S3-E3
Other mistake: Her name in the show is Elise Taylor, but on a badge in her car it's Elise Smith.
Factual error: The digital time zone clock on the wall in the FBI operation center is wrong. The show is set in NYC, which is Eastern Time. The clock shows EST at 16:44 and ZULU time (UTC / GMT) at 20:44. The difference between EST and ZULU time is 5 hours, so the clock should show ZULU time as 21:44. Plus, the times for the other time zones on the clock are wrong by an hour. (00:18:29)
Plot hole: When Scola and Nina enter the suspect's apartment and begin the search, Nina, before she enters one of the rooms says to Scola " come in here you should see this" indicating that she was aware of something important in a room that she had not yet been in.
Character mistake: The team identifies a blue Lexus fleeing the scene of the murder, but later in the show OA says to Maggie that they've located the black Lexus.
Undisclosed - S2-E7
Other mistake: Toward the end of the episode the perpetrator is corned by the FBI. He steps backwards from the curb and is killed instantly by a garage truck moving at a high rate of speed. In the following scene the garbage truck is shown just a few steps beyond the scene just behind a parked car. The truck was going very fast when it killed the perp and could not have stopped so quickly. Further it would not have been going that fast in a curb lane with a parked vehicle right ahead of it.
Compromised - S1-E9
Character mistake: When she and OA meet Marshal Ackerman, Maggie is somewhat surprised to learn Damon Cruz was a federal witness. As a federal agent herself, Maggie surely would know that the Marshals Service's mandate includes the witness protection program.