As Kenneth More is playing poker with the mayor and other townspeople, the number of coins on the table in front of him suddenly changes as he rakes in the pot while the camera angle shifts.
Kate shows Tibbs how to shoot, demonstrating by shooting two sticks in a river. The second demonstration is the same footage as the first.
During the pursuit of the stage coach by the Indians an arrow hits the side of the stage even though the Indians were NOT to the side but trailing BEHIND the stagecoach. Once again Hollywood can cause the laws of physics to bend to its will. In this instance it caused arrows to make 90 degree turns in midair.
Kate and Tibbs are by the river so Kate can teach him how to shoot. When she tosses the first stick in the water, she is holding her gun about waist level, ready to fire. The camera cuts briefly to the water to show the stick landing, then cuts back to Kate, who now has her elbow bent with the gun up by her face.
The actors playing Indians in camp are seen using modern fiberglass re-curve bows, and knocking their arrows on the wrong side for firing.
The clerk/gunsmith in London tells Tibbs that the derringer he is working with is the same model of gun that shot Lincoln. The Derringer (two "Rs") shown is a Two Shot Over and Under barrel pistol firing Fixed Ammunition (Bullet, Powder, Primer in a metal case). The gun that assassinated Lincoln was a single shot Deringer (one "R", not two) Caplock, that fired a bullet in front of wadding that was in front of Black powder and set off by a cap outside the chamber/barrel.
When Kate is teaching Tibbs how to shoot by the river, she again tosses a stick in the water and shoots her gun. The sound of the gunshot is heard immediately, but the stick does not break until a moment later. At that short distance, the breaking of the stick and the sound of the gunshot would be simultaneous.
At the river bank practice session the gun that they are using is a Double-Action revolver that has been made up to look like a single- action revolver of the correct period. It has a modern Cylinder Release, a modern ejector rod, and when they fire, they pull the trigger without cocking the hammer which would be necessary with an actual single-action revolver of the time period.
Kate refers the the surrounding area as the "Pecos country", which places the location in the Texas / New Mexico area. The last Indian raids in that area took place in 1875. However, when Kate is teaching Jonathan to shoot, she is using a swing cylinder double action revolver, first introduced in 1889 (and the model she's holding clearly uses a 20th century cylinder release).