Reid makes an incision in the hijacker's forearm, but in later scenes, the hijacker's forearm has neither a bandage nor an incision.
When the team pulls up to the scene, you can clearly see that Morgan is driving. However, when the team gets out of the SUV, Hotch is in the drivers seat and Morgan is in the passenger seat.
Toward the end, the unsub on the train shoots the FBI phone. From the first camera angle, the phone is clearly damaged and the receiver is no longer in place. A second later, from the next camera angle, the receiver is now undamaged and right where it was before the phone was shot.
There are many errors in the Texas drivers licenses shown. A standard drivers license would be Class C, not class 0; the seal is wrong; a license always expires on the birth date of the holder; the numbers are inconsistent with the dates they were likely to be issued given the ages of the holders.
The train used in the series is clearly not the Amtrak type train that would be used for passenger transport. Since 1970, the only long distance rail transport that is not part of an urban transport system (such as the MTA in NY and Connecticut) has been Amtrak and it uses a specific of locomotive engine and passenger car.
All of the passengers' clothes on their IDs are the same clothes they're wearing on the train.
After the team arrives at the scene, multiple cops are shown with their weapons pointing to the train. In one scene, you can clearly see a red tip on the barrel indicating a fake gun, most likely a child's toy.
As the team is driving to the train, Gideon tells Hotch to turn on the lights and sirens. In a scene of the SUV just before that, the headlights were flashing, as well as the red and blue lights on the front grill. Normally, they don't have them already on unless there is traffic.
When Ted shoots the guard on the train (twice, point blank, in the stomach area) You can clearly hear the gunshots, but there are no bullet holes, or blood, on the guard, even after he falls down between the seats. Nearly ten minutes in, we see the guard again, with blood on him and one bullet hole.
An establishing shot of the FBI command van not long after the BAU team arrives clearly shows a camera crew and boom operator working with an actor at the opposite end of the van.
The train is going from El Paso to Dallas, but a sign on the train shows a map of the Washington DC Metro system.
Garcia mentions that one of the hostages is from Adobe Walls at Terlingua. Terlingua is a ghost town near Big Bend National Park on the Mexican border. Adobe Walls is a historical site in the Texas Panhandle over 500 miles away.
The train supposedly travel through West Texas. However, the BAU team drives to the train through orchards and past mountains, neither of which are present in that region.
There never have been direct flights from Washington D.C. to El Paso. In fact, most of the flights to locations in Texas route through either Houston or Dallas which are major hubs.
If Elle was going to both El Paso AND Dallas, she almost certainly would have landed IN Dallas from Washington D.C. and had to catch a flight TO El Paso. The train ride would be illogical as she was already where she needed to be when she arrived in Texas.