When Uncle Jim starts pouring a drink for Old Timer, he is holding the jug handle with his right hand. But in the very next shot, only a second later, he is now holding the handle of the jug with his left hand.
When Uncle Jim is reading the nameplate on his new rifle, his hand is right on the backside of the part with the nameplate. Then, in the closeup shot of the nameplate, his hand is suddenly gone.
At the beginning, when Old Timer is removing the porcupine quills from Brighty's muzzle, he says "Why danged if you ain't grinning!" Right after he says this, his position in front of Brighty changes from crouching to a standing/leaning position between shots.
When Jake Irons and Brighty are crossing the Colorado River in the cage, Brighty freaks out and starts kicking at the wooden cage door. Before he starts kicking, the door is seen to be firm, intact, and unbroken, but in the shot of his first kick, you can see that before the hoof impact the door is already somewhat broken.
At the beginning, right after the opening credits, Old Timer picks up a gold rock. When he first picks it up, we see a close up shot of his hand holding it only an inch or so above the ground. The very next shot a second later, from the side, shows his hand holding the gold instantly a foot or so above where it was before.
When Old Timer strikes it rich and digs his gold mine, the rock he is digging and mining is obviously not gold, just ordinary rock.
When Jake Irons kills Old Timer, and he picks up the body right after killing him, you can see Dick Foran (the actor who plays Old Timer) grab Irons' arm before Irons drags him away.
When Uncle Jim and Homer are heading up the rim to report Old Timer's possible murder, we see Brighty running along the trail ahead of them and Jim and Homer riding along behind struggling to keep up. Jim and Homer stop briefly, Jim asks Homer for a canteen, then for some unknown reason Jim dismounts and leads his mule in the direction opposite to which they were heading before.