Several times in the movie in close-ups of the cops driving in their car, rows of houses behind them are visible out the back window of their car, but in the immediate next wide-angle shot they're out in the wooded countryside, with no houses anywhere in sight.
At around 19 mins: Close-up shots of Deputy Ramsey show the red lights on top of his car blinking. Long shots of the car show them off.
After the killer is shot in the left leg by the police on the other side of the moving train, he falls and there is blood on his jeans from the shot and also on the left side of his hood. I assumed the blood got on his hood because he touched it after grabbing the bullet wound on his leg, but in the next scene, when he jumps into the shallow water, there is absolutely no blood on his hood.
Eddie LeDoux confesses to the five killings in Texarkana at a point in the film when there had only been four murders.
When Peggy and Roy are leaving the prom, Roy is carrying Peggy's trombone case through the gymnasium. When they're outside and walking to their car, he doesn't have the trombone, but when it cuts to them getting into the car, the trombone is back in his hand.
At the beginning of the movie a graphic is put onto the screen to draw attention to the fictional date of the first attack. The graphic reads "SUNDAY, MARCH 3". Later, as a lead-in to the second crime, the graphic "SATURDAY, MARCH 24" appears on the screen. The narrator's voice adds, "Now, it is a rainy Saturday night, March 24, 1946, 21 days after the attack on Lovers' Lane." 21 days from March 3 would indeed be March 24, but it also would be (and was) a Sunday, just as March 3 was. The second graphic and the narrator's script were incorrect.
A caption places the Perot Theater on the Arkansas side. It is, in fact, on the Texas side.
Following the second attack (the first attack that resulted in murder), the narrator indicates that stock at all the gun stores was sold out by Monday (day after the attack) and that by Tuesday, May 26, locksmiths were overwhelmed with requests for their work. The attack occurred on March 24, so the date should be March 26, not May 26.
When the Texas Ranger arrives in the train station, he goes to buy cigars. The counter has a sign in front that says "ORANGES", written by a Magic Marker or marker-style pen. Sharpies or Magic Markers had only been created a year before and were not in popular use until the early 1950s, so a sign-painter would probably have painted the sign.
On several occasions, the killer is shown using a revolver with a silencer attached. Standard revolvers cannot be silenced. However, gas-sealed revolvers can indeed be silenced.
Obvious day-for-night effect when Deputy Ramsey finds the first murdered couple. Trees don't cast shadows on rainy nights.
During the quick wedding scene at the very beginning, the extra playing the new husband is obviously waiting for his cue to exit the church: he's looking down with a serious expression while everybody else is at least smiling or doing something to act like it was a wedding.
In the sheriff's office are some shots of the bulletin board in the background. On the board is the FBI's Wanted Poster for Frank Morris, following his escape from USP Alcatraz. The Alcatraz escape took place in June 1962, 16 years after the events in the film.
Linda Mae Jenkins is shown in the hospital with an IV line and drip chamber made of clear plastic. It's supposed to be 1946; that kind of IV line would not be invented for years. It should have been shown as made with latex rubber.
The film is set entirely in 1946 (just like the real killings) aside from ending narration from the present day. However, when the students are attending the Junior/Senior Prom on April 14, 1946, a banner at the prom congratulates the Class of 1946-1947. As the prom is being held in the spring semester of 1946, the graduating class would instead have been the Class of 1945-1946.
Closeup camera crew visible on a flatcar during long shots of the train.
When the cop grabs the suspect "Eddie LuDoux" by his belt and
pulls him over to the police car, the cameraman's shadow is seen on them as they walk across the frame
Obvious fire-hose rain coming from the left when Emma Lou Cook's boyfriend's car is leaving the restaurant.
Cameraman and his camera reflected on the wagon train during the slow-motion final chase.
When the law men are chasing the suspect and firing under the moving train which is showing in slow motion, it's easy to see the cameraman on the flat empty carriage getting his shot.