In the end of season 3 Jimmy takes his wrist guard off and throws it on the ground before he gets on the bucking horse. Then when he is found on the ground in the season 4 opener, he is laying there and has the wrist guard on his wrist again.
During the Season 3 finale, Jimmy takes his wrist brace off to bronc ride the horse that injures him for the 2nd time. When Season 4 shows the aftermath from the finale Jimmy is seen wearing his wrist brace while he is found unconscious in the riding pen.
When Roarke gets bit by the snake, it shows his hat fall in the river. When Roarke is running away, his hat is on his head.
SPOILER:Rip tosses a rattlesnake at Roarke that Rip has brought down to the stream in a cooler. Roarke, who is fishing in the stream at this time, is subsequently bitten by the snake high on the left cheek, less than an inch below his left eye. Roarke then runs about 50 yards up the hill in a panic before he falls while clutching his chest, gasping, and foaming at the mouth. His death takes about 45 seconds.
While rattlesnakes are venomous and occasionally poisonous, their bites are rarely fatal. When they are, it generally takes 6 to 48 hours to kill the victim, as the venom kills by shutting down the body's organs and acting as an anticoagulant. All of this takes some time to affect the human body, it is not immediate. Even if injected directly into an artery, death takes hours. However, the facial and labial arteries in the cheek that could rapidly transport the venom don't extend that far out on the face, thus making Roarke's rapid death even more unbelievable.
None of the assailants inside of the van were shown to be injured when Kayce Dutton rams into them even though they had to be unbelted while traveling in the cargo area. In fact, they seem to have been unfazed as they exited the vehicle quickly while firing in the exact directions that their law enforcement pursuers were parked,
When Beth's back is seen, she is covered with scars which are consistent with burns. However, the explosion would have concussion or laceration type injuries. Also, when the bomb exploded, she was facing towards it and should not have had back wounds.
Airbags were standard in Dodge Rams by 1998, over twenty years ago. Yet, when Casey's Dodge Ram hits the van carrying his father's assailants at a very high speed, no airbags deploy. Undoubtably, this is because a deployed airbag would have "punched' Casey, which would have stunned him to some degree. Also when he would have regained his senses, getting out of the truck in a rapid manner would have been extremely difficult as the deployed airbag would have blocked his egress.
During the flashback, at ~18:47 the cattle have modern day livestock tags.
When John Dutton is returning to the ranch in an ambulance, the word 'AMBULANCE' is written where it can be easily read looking at the vehicle. With ambulances that have their signage correct the word 'AMBULANCE' is printed in reverse so it can be correctly read in the rear view mirrors of vehicles in front of it.
The child whose mother was killed when John Dutton is shot is forgotten by the narrative. He's not in the truck with Rip and John Dutton when Rip is driving to meet the careflight helicopter. Nor is anyone shown to have stopped to take care of him when Rip stops to help John.