The design of Lisa's braces keeps changing.
When Burns asked Smithers where the union rep is, they are speaking over the intercom. However, immediately after the cutaway, Smithers is standing next to Burns in his office.
The nitrous oxide cylinder at the end of the episode is marked N²O. Chemical formulas use subscript for numbers, at least nowadays (the original Berzeluis notation used superscript and was still used during the first half of the 20th century).
The cover of Dr. Wolfe's picture book features an extra "of" in the title: "The Big Book of of British Smiles."
When Brockman says, "Homer, organized labor has been called a lumbering dinosaur", and also when Homer screams afterward, what they are saying does not match their lips, possibly indicating that this was dubbed over a different line. This is especially noticeable because when Homer screams, his tongue does not wiggle out of his mouth like it usually does.
When Lisa sings the strike song the first time, her lips don't match the lyrics of the song, suggesting the original dialogue was changed.
Homer scolds Carl for making him lose his train of thought. But Carl isn't the one who dropped the pencil into Homer's butt crack.