When Rat and Stacy are sitting on Stacy's bed, the page with the picture of Mr Deacon is the one open as they start kissing. When they sit up so Rat can leave, there is a different page open in the picture album.
When Mr. Hand is yelling at the class for failing his test, he re-teaches and tells the students that the Platt Amendment is an Amendment to our Constitution and is vital in their daily lives. The Platt Amendment is neither a Constitutional Amendment nor is it important in Americans' daily lives. The Platt Amendment established Cuba as a US protectorate after the USA helped free Cuba from Spanish rule during the Spanish-American War. Mr. Hand also says the Platt Amendment was passed in 1906. It was passed in 1901.
At one point, Brad claims he has to work before school. But this is during the part of the movie that he works at the seafood restaurant. No fast-food restaurant like this would be open early enough that someone has to work there "before school." One possibility is that the scene was originally meant to be put later in the film when he got the Mi-T Mart job. This theory is backed up in the alternate broadcast version where Hamilton is in a guidance counselor's office talking about his future and he says "I get up at 5:30 to go to work at Mi-T Mart, THEN I go to school, THEN I go back to Mi-T Mart!"
In the pizza parlor, Rat asks for Stacy's phone number. She produces a pen from her apron and before she even checks, asks Rat to borrow his pen because hers doesn't work. How would she know it doesn't work without trying it first? And IF she knew it didn't work because of the last customer, why would a waitress knowingly carry around a pen that doesn't work?
At the beginning of the film when the kids are buying the tickets we are told that the tickets would normally be $12.50 (so we know two of them would be $25). The tickets are sold for $20 each ($40 total) and he says he made $16 when actually he only made $15.
When Stacy is waiting by the curb for Damone to pick her up, Brad's car is clearly not in the driveway. However, when Stacy hears Brad's car start she runs outside to catch a ride with him and his car is just backing out of the driveway like it had always been there.
When Brad is next to the pretty girl in the Corvette, as she pulls away, you can hear the sound of the Corvette engine. In the next shot, from the interior of the Brad's car, we see the street directly ahead where the Corvette should be seen pulling away, but the Corvette is not there, even though the revving engine sound is still audible.
The big football game with Lincoln High takes place well into the Christmas season, as indicated by the decorations at the mall and All-American Burger. High school football season is generally over by early December, at the latest, and homecoming games (which is what the game between Ridgemont High and Lincoln High is supposed to be in the film) take place during the middle of the season which should be in October or maybe early November at the latest.
When Spicoli is in the convenience store with Brad, after saying, "I knew it," Spicoli reaches down off camera and picks up something and you can hear him place it on the counter, but in the next shot there's nothing there, he then picks up a can and puts it on the counter again.
When Damon takes Rat to get Stacie's number, the camera shows a quick shot from far away of Stacie leaning over the counter next to the cashier. Stacie's hair clearly has a braid running down the side. But as soon as Rat comes up to talk to her, her hair simply has been pulled back by barrettes. Her hair style is clearly different.
When Mike Damone gives Stacy Hamilton a ride home he acts as if he's never been to her house and doesn't know she has a pool, but in an earlier scene Mike and Mark show up at Stacy's house and end up swimming in the pool.
When Spicoli has the pizza delivered to Mr. Hand's classroom, the girl sitting on Stacy Hamilton's left hand side is wearing a gold necklace and then is not. Also, her hair is both tied back and hanging down throughout the scene.
After the pool scene, when Stacy is in Mr. Hand's class, she is doodling in her notebook. The pen she is using in the close-up is a Bic "crystal" pen, but when the camera changes to her sitting in her desk, she is using a different Paper-Mate brand pen. Also, the notebook is folded back, under itself, but when the camera is panned out, the notebook is open with two pages showing.
When Mr. Hand is asking Spicoli about his truancy, he writes, "I don't know," on the chalkboard. As he does this there is a shot of the class where Stacy is wearing a completely different outfit than in the rest of the scene. It is established that she is wearing a brown sweater, beige pants and a brown headband, but in this one shot she is wearing a red vest over a pink shirt.
Before Ratner approaches Stacy and asks for her phone number, a customer in front of her is ordering a slice of pizza. In the close-up shot, there is a pen next to the order tablet. In the next shot, the pen is gone and the pizza is in a different position.
As Mark approaches Stacey in the pizzeria to ask her out, she is cashing out a customer's order. He gives her a bill and a coin. She says, "$1.10 and you get five cents back." There is no way a nickel could be correct change.
Linda dives into the pool, makes a sharp turn to the right, and uses the ladder on the side of the pool to get out (complaining of water in her ears). The turn, while cut a bit short, is not impossible.