Mark is shown lying on the ground. The camera then scans up and shows the cougar above him in the tree. However, it is obvious that during the scan it is not one continuous shot and thus the cougar is not really in the tree above Mark.
When Lucas is tracking the cougar and Ben (Lou's friend) sneaks up behind him, Ben throws a rock into the water to get Lucas' attention. However the rock comes from Lucas' right side, and Ben is standing behind Lucas.
When Lucas finishes speaking to Micah, moments after Lucas and Ben have their altercation in the street, Lucas gets ready to mount his horse. As he puts his foot in the stirrup and swings up onto his saddle, the saddle shifts horribly to the right under his weight. He then rides out of sight with his saddle still obviously very loose, and leaning badly to the right.
After almost getting into a gunfight, Lucas gets on his horse and rides out of town, , apparently to hunt down the cougar. As Micah and Lou are talking in front of the hotel, you can see over Lou's shoulder that the horse has stopped just off set and Chuck Connors leg swinging over the horse as he dismounts.
When Lucas scolds Mark for not staying with the horses, Mark says, "I just came over here 'cause it was shady." However, Mark was never in the shade and was sitting in the sun the whole time.
At the ending scene, when Chuck Connors sits down to take off his shirt, the barrel of the rifle is pointed right at him. Any owner of a firearm knows to never have a barrel pointed at anything you do not intend to shoot at.