Other mistake: When Morgan is showing the rest of the team the drivers license photos of the hostages on the train, every one of them is wearing the same shirt as they are on the train.
Character mistake: Close to the end of the episode, Dr. Reid says to the psychotic guy that was holding hostages, "M-theory cannot be proved." It should be "proven, " not "proved." Dr. Reid is supposed to be a genius, so he should be the last one to make such a mistake.
Visible crew/equipment: When the camera zooms in on Adam's body near the start, there is a very brief shot of a crew member's hand in the top left hand corner of the screen. (00:02:35)
Continuity mistake: In the scene just after Gideon talks to Cherish's mother we see him start to walk toward the rest of the team. In the wide shot we see Reid standing with his hands in his pockets and jacket open, we then see him close his jacket and cross his arms as Gideon gets closer, but in the very next shot (the close up on Reid) we see his jacket open and his arms at his side once more. (00:12:20)
Continuity mistake: When Reid is asked if he plays ball, the way he holds the football changes between shots. In one shot he holds it in 2 hands and in another he holds it in one hand. (00:14:30)
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)
Continuity mistake: In the scene when the investigators at the police station realize who the killer is, the deputy enters and says that a revolver is missing. However, when Cory pulls out the weapon in the woods, he is holding a semi-automatic pistol. The deputy would know the difference between the two, but still uses the wrong term (a revolver may be referred to as a pistol, but an automatic like Cory had stolen can never be called a "revolver", as the chamber does not revolve).

Continuity mistake: In the scene where Gideon realizes the unsub is a cannibal, Garcia enters the office behind him and shuts the door. In the next shot, the door is wide open. (00:13:40)
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.
Factual error: In the episode, the case is handled locally by the Wilmington Police Department. In reality, Wilmington Police only operate within city limits. Based on the suburban locations pictured, this case would more likely be handled by Delaware State Police or New Castle County Police.

Deliberate mistake: When talking to Sarah Jean's mum, the bottle of Smirnoff vodka is missing the 'S'. (00:09:35)
Continuity mistake: In the opening scene (after the credits), Elle's hair is in bangs. In the scene where they discuss the killer using zip ties instead of ropes her bangs have suddenly grown in. (00:05:05 - 00:15:45)

Visible crew/equipment: After the BAU capture "grandfather," when Hotchner has Reid on his cell's speaker, just as Reid says, "He spent 22 months in prison...," we can see the shadow of the boom pole and mic on the ground behind Hotch. (00:33:50)

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
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
Character mistake: In the initial meeting at FBI headquarters, the agents mention the Zodiac killer. Gideon says about him "Yeah, and he killed for 30 years without being caught." In actuality, the Zodiac's known victims were killed between 1966 and 1970. In letters to the public, Zodiac claimed responsibility for several other murders (most of which were solved without being attributed to Zodiac), but no later than 1974. Gideon's statement was off by at least 22 years.
A Real Rain - S1-E17
Continuity mistake: When Gideon puts on a glove to examine the flint blade from the fourth victim's head, the glove snaps and breaks. In the next shot, more close up, Gideon's glove is not broken.
A Real Rain - S1-E17
Continuity mistake: At the end when the FBI is going to the apartment where the killer is holding the hostages, Gideon puts on a bulletproof vest while standing next to the car talking to the cop and a second later while he's walking toward the building he puts the vest on again.
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.
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.