(At around 1h 19 mins) In the final scene in the Medieval throne room, the position of the queen and the knight on their seats changes from shot to shot, and the knight's hand moves from palm up to palm down. This can be explained as the Queen and Black Knight depleting their stored charges. They lack sufficient power to interact with Richard Benjamin, but have enough to attempt to move.
(At around 57 mins) During the fight between the Medieval Knight and the Black Knight, the bent sword switches between characters several times.
(At around 28 mins) When the robots are loaded onto the conveyor belt to be repaired at the end of the day, the first one, a man in an orange shirt, has his hat on his chest. In the next shot, it's on his head.
(At around 17 mins) The first time Peter shoots The Gunslinger in the saloon, the exit wound is in the center of his back; when he turns around, the entry wound is in his right shoulder.
After the Chief Supervisor orders a power shutdown, accidentally locking himself and the other technical personnel in the control room, Peter finds them all dead of suffocation. The amount of real time that expired was less than an hour, and the technical personnel couldn't possibly have suffocated that quickly.
(At around 40 mins) When Peter blows out the wall of his cell with explosives, the explosion was so powerful that the concussion would have killed him or anyone else in the cell.
(At around 1h 9 mins) When Peter is escaping Westworld, he passes by a sign that says "Leaving Westworld" with several iterations in different languages. The French version says "Vour" instead of "Vous" and "doivant" instead of "doivent".
(At around 2 mins) The opening commercial for Delos refers to traveling there by Hovercraft. However, the cabin shots of the transit vehicle show that the vehicle is capable of banking from relatively high up. Hovercrafts travel at a fixed low height above the ground and don't bank, therefore the transit craft must be an aircraft of some kind.
(At around 40 mins) When Peter exits his jail cell after the explosion, he has no dust or debris on his clothes.
(At around 1h 17 mins) The Gunslinger's clothes are unaffected after being splashed with hydrochloric acid. However, some fabrics are hardly affected by hydrochloric acid.
The Gunslinger is able to track hoof prints using infrared, despite the fact that the horses in Westworld are robots and have no body heat. However, given that The Gunslinger only started seeing Peter's body heat (rather than colors that correspond to reality) after the acid incident, it is clear those must be different marks. This also explains why he didn't spot Peter right away in the repair room.
In the Western resort, the guns have a heat sensor which makes them impossible to be fired at a guest, who would be warm-blooded; the robots are not. Without body heat, the "interactions" with Miss Carrie's girls would be somewhat uncomfortable. However, exceptions can be made for the prostitutes since they are never supposed to be involved in gunfights anyway.
(At around 1h 24 mins) The robot girl in the dungeon shorts out when Peter gives her a drink of water, yet the robot Miss Carrie was seen drinking whiskey earlier in the film with no ill effects (at around 51 mins). However, some robots were simply designed waterproof while others weren't.
The Wild West resort is sometimes called Westworld (as in the opening promotional film with guests being interviewed, or on the multilingual sign as Peter tries to outrun The Gunslinger) and sometimes called Western World (as in the orientation film shown on the hovercraft, or on the color-coded tram ride to the resort). However, that's because they are both valid names for the park, with "Westworld" the catchier alternative.
(At around 1h 22 mins) In the throne room where Peter has the confrontation with The Gunslinger, the Black Knight can be seen breathing, although he is supposed to be an android with a dead battery.
(At around 36 mins) When Peter kicks in the bedroom door, he fires more rounds than the revolver's capacity.
In the multiple scenes where the staff in the control room are worried about not being able to open the doors because all power is lost, computers in the background are still lit up and blinking and old-style tape units are spinning.
(At around 40 mins) When Peter blows up the jail wall to escape, you can see the intact part of the wall undulate. Real brick and mortar are not flexible and would not behave in that manner.
When The Gunslinger is chasing Peter, the monitor in the control room pans to follow him, despite the fact everybody in the control room is dead.
The explosion makes the entire jail expand and contract like in a cartoon, revealing that the walls are anything but solid brick.
(At around 18 mins) When Peter demonstrates the gun's inability to fire on humans in their hotel room, the hammer hitting and the click sound are not in sync.
Guns in Westworld are equipped with sensors to prevent a guest from shooting another guest. No explanation is provided for how guests are kept from harming one another with the swords and daggers from Medievalworld and Romanworld or with fists and furniture in Westworld (as in the barroom brawl). The same goes for the explosion created by Peter to bust out of prison.
It seems very unlikely and highly illogical that the control room would be airtight. For what reason? And why would there be no fail-safe way of opening the doors in the event of a power failure? Also, the control room would also likely have some form of air conditioning, indicating some form of ventilation or air ducts so that there would be no way for the technicians to suffocate.
The Gunslinger manages to fire his weapons many times without having to reload them.
No explanation is given on how guests are prevented from being outside all night. One cannot pretend that the guests are kept indoors and away from windows.
If it is the park's claim that no visitor can be harmed by any of the robots, it seems implausible that the Gunslinger would be armed with any weapons loaded with live ammunition capable of killing anyone.
(At around 1h 13 mins) When Peter discovers the control room, he doesn't even try the door. For all he knows, the people he sees are simply unconscious and could be revived to help him, or there could be something else useful to him in that room, but he just looks in the window and walks away.
(At around 56 mins) The Black Knight calls the guest out by calling him "thy scurrilous knave" instead of "thou scurrilous knave".
After the Gunslinger kills Blane, he allows Peter to live long enough to escape when he could have killed him right there.
The management of the park would never allow a guest, with no apparent experience in its handling or use, to obtain, plant and set off enough dynamite to blow up part of an occupied building with other guests randomly wandering around town.
When Peter figures out that the Gunslinger used infrared vision to attempt to track him, he also figures out that he cannot be detected while standing next to the torches. Peter then lets out a sigh, which the Gunslinger hears but cannot pinpoint. Then, Peter kicks a metallic object on the ground, to which the Gunslinger reacts to before Peter sets him on fire.