During the rodeo scene you can clearly see a 48 star flag (6 rows x 8 columns). If this area is still a territory, we know it's not Alaska or Hawaii. Before Arizona and New Mexico became states, there were 46 stars.
In the scene where John Wayne is hunting with a shotgun, you see him reload the shotgun, but it appears that the shotgun shell that he is using is a plastic hulled shotgun shell, not the paper ones or wax impregnated paper ones that would have been common during the time when this movie was supposedly set. In fact, plastic hulled shotgun shells did not come around until Remington introduced them in 1960. Remington used green plastic in their shells, so the moving was more than likely using a modern Remington plastic hull shotgun shell.
SPOILER. When McLintock shoots Devlin Warren, we see a close up of Devlin as he raises his hands and backs away. We can see that his right hand is clearly empty in this shot, but in the next shot he's holding his hat in his right hand as he falls.
At the start of the "the hell I won't" scene, just before Jones (Leo Gordon) pushes at Wayne with the shotgun, McLintock's (John Wayne) pants are clearly wet up to his knees, as if he had been walking around in the water at the bottom of the mudslide. The next shot the pants are dry.
In the long fight scene at the end, Katherine flies out of a window and lands in a trough of water. After that, trying to escape G.W., she falls into the dusty and muddy road. But still, in the next scene her underwear are clean white - and dry.
A tipsy McLintock is trying to walk Katherine upstairs while swigging from a full whiskey bottle. They fall to the bottom of the stairs and the bottle clearly spills. Katherine picks the bottle up and bops McLintock on the head with it, then it amazingly becomes a full bottle again just before she throws it against the wall and it shatters.
When Agard falls from his horse, his glasses are on his face at an angle. When getting lifted up he has them in his left hand. But when he gets into the buckboard they are back on his face at an angle again.
After the mud fight when Mrs. Warren is carrying Katherine's breakfast tray the teapot spout is pointing to her right at the bottom of the stairs but is pointing to her left when she knocks at Katherine's door.
After McLintock hires Dev Dev rides a horse to the encampment. First the animal is wearing full harness, next Dev mounts and as he rids away there are stirrups visible; last view entering the camp Dev seems to be riding bareback - no harness under his seat.
At the beginning of the movie when GW and Drago leave in the buggy, the back cushion of the rear facing seat in the buggy falls out of place when they take off. When the camera angle changes the seat cushion is now back in place.
In the opening credits there is an artist's rendering of the town of McLintock, with signs for every building indicating that every business in town is owned by McLintock. The sign on one of the buildings misspells McLintock as "McClintock."
After McLintock hires young Devlin, McLintock drives off with Drago sitting to his left. The wagon turns around (off-screen) and heads out of town. After the off-screen turnaround, the characters have traded places in the buggy and Drago is now on McLintock's right.
When G.W. is dancing with Mrs. Warren at the party, and Ben Sage sees Katie watching them from a distance and getting jealous, he is several feet to Katie's left. When the camera angle changes, he walks up to Katie from the opposite side, on her right, to talk to her.
In the mud hole after Kate turns and trips over the Indian agent she is shown face down in the mud with the nearest person behind her standing. Just after she stands up you see the Indian agent getting up immediately behind her.
After Katy is covered with molasses and feathers, including her hair, in the Indian "attack" scene, McLintock goes to see her 5 minutes later and she greets him with clean dry hair and skin, wearing new corset, slip, etc. While she might have been able to change her garments in that time, there is no way she could have gotten molasses and feathers off over even her hands, much less her hair, in that amount of time.
In the famous chase scene near the end of the movie, when Katherine tries to escape from G.W. into an alley behind the general store, the shadow of the camera as it zooms in for her closeup is clearly visible against the store wall on the left side of the shot.
The goof item below may give away important plot points.
When GW shoots Devlin Warren, the shot appears in the middle of his stomach as he is backing away. When the camera changes and Dev is sitting on the floor, the shot is higher and to the right, on his left breast.