After the policemen arrest Miss Ackerman, Freddie says that maybe they should tell the principal. That is a mistake because to arrest someone in the school, the policemen have to already have permission from the principal.
A sign on the whiteboard in Ms. Ackerman's classroom reads "State claims to land in the west in 1776".
Spencer calls people from Thailand "Thailamanians". They are actually called "Thai".
When Ms. Ackerman comes over for the first time when she is wearing the red dress, she notices that Spencer's "soup" is boiling over. With the pot that Spencer was using, he would have easily burned his hand.
In the opening sequence, after Sam knocks down three bowling pins, the two remaining pins are located right at the far corners of the blue floor tile, but after the discussion concerning Miss Ackerman and Sam attempts to knock them down, both pins have moved.
When Ms. Ackerman gives Spencer the PearPod, the box says PearPhone, although there's a chance that Ms. Ackerman placed the PearPod on a PearPhone box, or that the packaging itself had an error.
Despite being a major plot device, downloading copyrighted music for free is not a crime. Rather, it is a civil liability to be sued by the music's copyright holder if one exists and the music was not officially offered for free anyway. It would neither involve the FBI nor result in arrest unless Ms. Ackerman was caught selling the music files for money to other people.
Why would Carly throw the PearPod to the FBI agent? If he hadn't caught it, it could've broken and destroyed evidence and Ms. Ackerman would've been released.