In "The Shore Thing," Arthur's dad's catering van is different than in previous episodes. Also, the back doors look damaged and bent out of shape. The doors also do not close all of the way either.
Brain no longer has hydrophobia, fear of water.
In "It's a No-Brainer," when Alan's brain is reaching for the binoculars, his brain's hands are suddenly brown. In the next scene, they are back to gray.
In "The Shore Thing," when Arthur, Binky, and Dad are on the boat, Arthur asks why they aren't heading up to shore. When they cut to Dad and he tells them it's a surprise, his skin color is darker than usual. Then after that, he's back to his normal color.
Mr. Ratburn: Define "hypontenuse".
(Buster buzzes in.)
Mr. Ratburn: Yes, Buster.
Buster: I... di... no... Did I do that?
In "The Shore Thing," Buster mentions Twenty Thousand Leagues Under the Sea, a novel by Jules Vern.