Continuity mistake: Near the end of the episode, when Mr Schue is talking to Terri in the school hallway, there are several people walking around in the background and there is even one student running towards the camera. In the next shot - one second later - the hallway is completely empty.
Deliberate mistake: When Howard enters Figgins' password to hack into his AOL account, Figgins' inbox is obviously visible behind the login box, which simply disappears once the password has been entered. In addition, look closely at the inbox and you'll see that not only is there no mail, they are actually in GMail (the logo has simply been edited out of the top corner).
Continuity mistake: While Santana is singing "Back to Black", Jessie is seen obviously scribbling something down. Yet at the end, his notepad is shown with a drawing of a cat upon it. If he was drawing the cat, he would have been drawing smooth lines, not scribbles, as the drawing contains no scribbles at all.