When Plummer's poker hand (aces and eights, the dead man's hand) is shown in close-up, the ace of spades shows that the deck is a Bee brand deck of cards, first produced in 1892 by the U.S. Playing Card Co. (Hence the "92" on the ace.) The movie takes place in approximately 1880, so these cards would not yet be available.
At Apache Wells where Chris rushes in to wake the Marshal to say his wife has run off, the Marshal and Ringo Kid are chained together at the ankle. The Marshal delivers his line but moves his chained leg too far, jerking the chains around Ringo's ankle. Ringo yelps and grabs his ankle. As the Marshal turns toward Ringo to undo the chains, the Marshal is clearly struggling not to break up laughing as Ringo glares at him.
In the fight between the stagecoach's passengers and the Indians, we see the same image of one Indian, with a lance in his hand, falling with his horse two times. One time shot by Marshal Curly and another time shot by Hatfield.
When Dr. Boone (Thomas Mitchell) first meets Peacock (Donald Meeks), he grabs a whiskey bottle out of his hand to "sample" it. After chugging what looks like a good portion, he hands back the bottle, which still has the same amount in it.
It's understandable that, in 1939, pregnancy was not a subject for movies. However, it's noticeable that Lucy Mallory, who is about to have a baby, wears a tight-waisted dress and shows no sign of being pregnant.
In the initial Indian attack, Curley uses his shotgun (which is also sawed off, as was the convention to serve as a "scatter gun" to spray buckshot). He manages to kill two Indians with two shots. These Indians are extremely out of range for the weapon.
In the beginning sequence when the stage is coming into town you can see that the buildings are stage facades as the camera shot is at an angle and it is clear there is no structure behind the false front.