The Fisher King: Part 1 - S1-E22
Visible crew/equipment: When Elle arrives back at her home the camera pans and you can see the face of a man in the mirror. A man who is not the Fischer King as he has no facial burn marks on him. Potentially simply a stand-in for the character or the actor without the makeup as when the Fischer King is going to shoot Elle you cannot see his face.
Won't Get Fooled Again - S1-E3
Audio problem: The video game Penelope is playing is supposed to be Tetris, but the sound effects are from the Atari 2600 version of Pac-Man. You can hear Pac-Man die four times during the scene. (00:12:20)
Revealing mistake: When Hotch and Spencer are interrogating Eddie, Spencer shows him the three photos of the people he has killed. Eddie makes a gesture as if to speak and points at Spencer, at which point we see a shot of Spencer and he very obviously glances into the camera.
Plain Sight - S1-E4
Continuity mistake: At the very end on the plane, Gideon gives Reid the two tickets as his birthday present. In the shot facing Reid, he holds the tickets facing himself. In the reverse shot, the tickets now face Gideon. (00:39:30)
Continuity mistake: Before the BAU catches the serial killer Carl Arnold, they used a heat sensor and it shows five people sitting at a table. They said there were three adults and two kids, but when they break in the house, the mother and one kid were sitting at the table, the father was tied up nearby, and Carl Arnold and the other child were in the basement. They were found by Derek Morgan right before Carl Arnold threw the child at Gideon, who fortunately caught him.
Continuity mistake: At the start, JJ puts a file down on the desk, and her left hand is in front of her, and she has 2 items in her right hand. When the camera angle changes to behind JJ, her left hand is now on her hip. (00:02:20)
Continuity mistake: When Reid disarms Maggie, he has his hand on the gun but no thumb on the hammer. When the shot changes to Maggie's POV, he has his thumb on the hammer. (00:37:20)
Revealing mistake: When the suspect is first put in handcuffs at the house, it's clear to see he is just holding the one cuff rather than wearing it. (00:27:50)
Continuity mistake: When Reid tells Lila that her manager is dead, he has his hands on the back of his neck. When the shot changes, his arms are now lowered and under the water. (00:27:00)
Continuity mistake: When Lila gets the note that was taped to her door, she holds it by the side in the close-up showing the contents of the letter and from the top when she is crumpling it up. (00:15:30)
Visible crew/equipment: When the suspect first enters the house, their helmet reflects all the camera and filming equipment. (00:04:20)
A Real Rain - S1-E17
Visible crew/equipment: In the suspect's apartment by the boxes, there is a green tape marker at Reid's feet. (00:35:00)
A Real Rain - S1-E17
Visible crew/equipment: When talking about the cop killer victim in the police station, an orange tape marker can be seen on the floor. (00:19:20)
A Real Rain - S1-E17
Factual error: When BAU walks up the stairs on the way into the courthouse the first time, the John Ferraro building in Los Angeles is visible in the background. They are walking up the stairs toward Los Angeles City Hall. The episode takes place in New York.
Visible crew/equipment: During the plane interior scene after the opening credits as JJ is walking around handing out documents to the team, you can see a gap in the lighting outside and a crew member's face peeking out from behind the white walls. (00:04:00)
Continuity mistake: When Gideon is talking when we first see him, the pictures behind him on the screen change instantly. It should be noted, that when we see the pictures change, there is the audible click and visual delay of a slide change which is not present on the instant change. (00:04:20)
Continuity mistake: Morgan gets a call from BAU and we see him holding his phone in one hand then two. (00:03:40)
Audio problem: As Scott McCarty is shot there is no sound of a shot being fired, suggesting a silencer, however as the assailant's rifle is pulled inside the car you can see that the weapon has no silencer.
Revealing mistake: We see the jet at the end, and the shot is flipped. Note the serial number on the plane's engine. (00:38:05)
Chosen answer: Black SUVs are common police, military and dignitary vehicles around the world. It is not too much to assume they could be rented or owned by the police forces in the areas.
kristenlouise3
Other people have explained it but fore more information, federal cars would most likely be brought to the airport from the nearest agency, so they can drive out to their locations especially in rural situations.