Wendy's coat changes color when she's laughing with others at Kenny's haiku.
The Planetarium guy says that he cannot pronounce the "t" in planetarium, and pronounces it "plane'arium". However on the return trip, he says "planetarium" normally.
When the class tries to persuade Mr. Garrison to take them back to the planetarium, he says that it's "right down the street" however, in the beginning, when they are headed there for the first time they are traveling down a highway towards Denver.
The dog star is Sirius, not Polaris.
Mr Garrison says they are going to watch episode #203 of Barnaby Jones, called "Barnaby Under Siege". There were only 178 episodes of the series, so 203 must mean season 2, episode 3. However, the correct title for that episode is "Echo of a Murder", and in fact there was no episode called "Barnaby Under Siege" at all.