In the song "Old Devil Moon" as Woody and Sharon dance through the stream, Woody has bare feet and his hands are in Sharon's. In the next shot, he has his shoes on, and it even looks as if his trousers are dry.
Before Sharon begins to sing her part during the "Old Devil Moon", she is lying down. As she begins to sing, she is sitting up, and then, in the next shot, she is lying down again.
When Sharon has finished washing her father's shirt, the front of her dress is wet, but when she meets Og the Leprechaun in the well, her dress is dry.
When Finian goes into the woods to bury the crock of gold, there is a shot looking down on him while he is digging the hole. It shows quite a lot of dirt between the pile of dirt he has heaped up and the hole, enough to cover up the grass immediately around the hole on that side. In the shot right after he places the crock in the ground, there is no dirt on the grass around the hole.
When Ogg is talking to Finian at the creek, he falls into the water. Seconds later, his hair is completely dry and combed.
Most of the cars in the film are from the late 1940s, indicating the movie is set when the play premiered (1947), but at the end of the "Begat" number, the gospel singers' car is being towed by a 1960s tow truck.
Thought to be an anachronism, at the end of the film, as the end credits appears, a Volkswagen Beetle can be seen coming along the road. The Volkswagen Beetle went into production in the 1930s, and so it is possible that there would have been a VW Beetle on the road during the 1940s setting of the movie.