During the barn dance after Gideon's axe jumping, he Daniel and Caleb dance with the girls until three townsmen jump from the roof and take the girls away. In the shot immediately after, Daniel has turned into Frank when they slide underneath the wooden beam.
During the barn dance, there is a part where Frank, Ephraim and Caleb are dancing with the girls, Frank is dancing with Alice and in the shot immediately after, Alice is standing behind Gideon at the side of the dance floor.
In the big fight and dance at the barn raising, the brothers change locations rapidly. Also, there are noticeable discontinuities during the acrobatic bits, probably because they needed some repeating.
During the "June Bride" sequence, one of the girls plucks a bunch of fresh flowers to signify a bridal bouquet from a container hanging on a post in the bedroom, but the scene takes place in the middle of winter.
After Millie and Adam's baby is born, we hear the baby cry after being slapped. The slapping of newborns originates in Victorian England when the sedation given to the mother also passed to the baby. The stimulation of the slapping is what caused the baby to take its first breath.
The brothers claim that there were no F names in the Bible. While there are "F" names in the New Testament, all the names shown are from the Old Testament, so presumably that was the only part of the Bible they were referring to.