During the sequence showing the mice are sitting in the audience/mousetrap, Tony, Bridget, and their baby only made a one-second view with the crowd, while in all other shots, they are missing from the crowd.
Tanya goes from barefoot to wearing shoes throughout the movie.
When Miss Kitty is applying blush to Tanya's cheeks, blue eyeshadow suddenly appears on Tanya's eyes as blush is being applied to her right cheek.
When Fievel says "Let's go on that ride again!" after the can goes down the last waterfall, his voice is sped up.
Tony Toponi's shirt and hat frequently changes colors during cameo shots. In first shot, his shirt is light blue and the belt on his hat is the same "red" color of his hat with the buttons missing. In second shot, his shirt is changed to dark blue and his hat belt appears black, revealing his gold buttons, which carries to the third shot. In fourth shot, both his shirt, hat and his head hair are changed to green, as his red scarf is strangely replaced with a white bow tie, notably another mouse (slightly older and not having head hair, setting between him and Bridget) is wearing a dirt-colored scarf and hat and a dark blue shirt (switching without audience looking). This is arguably because of Tony's role limitation in this film from Pat Musick's involvement with several other works at the time, causing the staff not to confirm (as unfocused) the exact palette for the character.
When the mice are sitting in the audience/mouse trap, Tanya begins singing "The Star Spangled Banner". The movie takes place circa 1885, and although the words to the song were written in 1814 by Francis Scott Key, the song was only used by the Navy in 1889, and didn't officially become the national anthem, and thereby most likely to be sung at public events, until 1931.
At one point in the movie, T.R. Chula is chasing Fievel and singing a taunting, sadistic version of the "Itsy Bitsy Spider" song. The song was first published in the form most commonly used today (with water spout, etc.) in 1962, and its earliest publication was in 1947. It's not likely the song was sung circa 1885, when the movie was set.
When Fievel rides the tumbleweed he goes past armadillos. Armadillos were not found very far north of Texas in the 1800s.
Characters can be seen going through Monument Valley (on the Utah/Arizona border) when they are supposed to be on their way to Green River (Wyoming).