Continuity mistake: Truly crashes into the pond three times: first when the kids are playing in the road and she takes them home, second on the day of the picnic when she says she has nothing else to do and will go on the picnic too, and third at the end of the film when Potts finds out he is rich. In the second of these three, when Mr. Potts carries Truly from her car in the pond, the end of the ribbons on the back of her dress gets soaked in mud, but when you see her again at the beach there is no sign of the dirt.
Factual error: In the famous tugboat scene, Fannie rides out on a New York Central tugboat painted jade green - a color which wasn't instituted on the boats until the early 1960s. To be accurate, the tugboat would have to have been painted red with a black stack and the New York Central logo.
Continuity mistake: When Finian and Og are talking in the forest, Og is kneeling on a log. He leans over and falls into the river. You can see him completely submerged. He stands up and continues his conversation with Finian while standing in the river and his hair is now completely dry.