In the scene where Mrs. March withdraws Amy from the school, Amy is shown eating what are clearly fresh-baked chocolate chip cookies. The chocolate chip cookie was not invented until 1930, more than half a century after the Civil War.
The opera which Jo and Frederick watch is Georges Bizet's "Pearl Fishers", which was first performed in Paris in 1863. However, the opera was not performed in the U.S. until 1892, long after the action of the film.
The lyrics to the carol 'Deck The Halls' as sung in the movie are a variation of the original English lyrics and were first printed as this variant in America in 1877, although without the third 'fa la la la la...'.
When Laurie receives Jo's letter in London, telling him of Beth's death, her voice-over says, "Please, Teddy, come back to us". But when we see the letter a moment later, it actually says "come back to me".
The soldiers' uniforms in the various party scenes have both stripes on the sleeves and shoulder boards. In reality, stripes on the sleeves denote an enlisted man, and shoulder boards denote an officer. They are thus mutually exclusive and both would not have been worn by the same individual.
When Amy has returned home after falling into the pond, Meg is seen hanging up her wet clothes. Meg remarks that she cannot believe Jo walked all the way home in only bloomers. Although Amy is the one who fell in, and this may seem an error on Meg's part, Meg means that Jo walked home in bloomers because she gave Amy her clothes in order to keep her warm.
When Jo tells the family she sold her hair for the train ticket, it looks as if her long hair is bundled under her wig. In real life, Winona Ryder's hair was very short and there were two wigs made for Jo March, one long and one short. What looks like long hair bundled up is really Winona's hair peeking out below the wig.