Continuity mistake: When Lamar is sitting eating in front of the black and white TV, he's sitting up and angled towards the guy next to him who he smiles at while holding his plate up. However when the camera angle changes, he's now slumped down and his plate is nowhere to be seen and he's facing forward.
Continuity mistake: When Gilbert is handed the mic to talk at the pep rally at the end, his left shoulder is covered with grass and dirt from being thrown on the ground. However when the camera shot shows him first talking to the crowd, all the dirt and grass is significantly less and even completely disappears once Betty and the rest of the nerds come up to join them.
Deliberate mistake: When Betty walks away from the kissing booth it is clear that she has spike-like heels on her boots. When she steps on to the "moon" surface the spike heels are gone. Her spikes are on up to the point where they enter the room. I am pretty sure the crew did not want to puncture the bladder and have water all over the set.
Continuity mistake: In the scene where Lamar is throwing the javelin, you can see the scoreboard for the games. The Tri-Lambs currently lead the games with 10 points (which was after the tricycle race), but at that part of the movie, the Alpha Betas currently led and had at least 40 points.