In the scene where Books and Gillam share a bottle of whiskey, as the camera changes angles the bottle label is always away from the camera.
When Books and Mrs. Rodgers are riding in the buggy after meeting up with Mike Sweeney, you can see the address numbers on the walls of the buildings they pass. There were no addresses on the walls in 1901.
In the scene where the two bad guys try to ambush Books while he sleeps, Books kills the first guy with a couple of gunshots, and the second guy waits a few seconds, then shoots at the bed again, as though no shots had been fired. In reality, he would have run away or shot at Books standing in the room.
When Books is in the barber shop talking to Mr. Beckham the undertaker, in different scenes Books' tie is either inside or outside his vest.
Books just finished a gun battle in the bar, and was shot by the bartender. Gillam runs in, grabs Books' gun and shoots the bartender dead with three more shots. Then he looks at the gun, and you can clearly see all the bullets still in the cylinders of the revolver.
Books tells Doc Hotstettler that "ten days ago, in Crede, Colorado......" and that he got on his horse and took off to find the Doc in Carson City, Nevada. That is about 600 miles away, which would mean riding 60 miles a day on horseback for a man dying of cancer and having trouble sitting without his "fancy pillow".
When Books falls in the bathtub, Mrs. Rodgers goes in to help him, and about three seconds later, he emerges from the bathroom fully clothed in his robe and a towel around his neck.
A couple of times in the movie, the camera pans to John Wayne, and his hair is parted on the wrong side. (Reverse editing flaw).