First Kiss - S2-E1
Plot hole: The story is about Lizzie's First Kiss, but in season 1 she kissed Aaron Carter under the mistletoe.
Continuity mistake: At the beginning of the episode when Kate is inviting Lizzie, Gordo, and Miranda to her party and they read the invitation it says she is turning 14 but in Season 1 Episode 30 Gordo's Video, in Gordos video Kate tells Claire she's already 14.
Suggested correction: Kate soon turning 14 is a running gag in the show. She is canonically hiding her real age, so it makes sense that she lied about her birthday party and only confessed to her best friend about her real age. This running gag becomes more clear when Mrs. McGuire asks how old Kate is turning, to which she replies with "14" and Mrs. McGuire starts chuckling and says "sure."
The Greatest Crush of All (aka My Love Is a Red Red Chimp) - S2-E28
Continuity mistake: During the scene where Mr. Keith introduces himself to the class and writes his name on the chalkboard, his name changes from underlined to not underlined between shots.