In the classroom, Casper ties Amber's shoelaces together before anyone else's. When Amber stands up to protest the party being at Kat's house instead of hers, she doesn't trip over them. She sits back down, but when the bell rings and she gets up, she trips.
When Stretch is "sword fighting" with Dr. Harvey at the stairs, Stretch holds a golf club. In the next shot, Stretch holds an umbrella up close. In the next shot, he holds a golf club again.
The amount of the 'resurrection liquid' changes from scene to scene.
The dust on the buttons on the Frankenstein book change repeatedly.
The Up and At 'Em Machine puts a bow tie loosely around Kat's neck. When she gets to the end of the ride, it's attached around her neck tightly.
When Casper grabs Kat's arm and drags her toward the window out of the room, she leans back and gets dragged on her heels, thus pulling her arms stiff straight out in front of her. Before they're out of the room, he starts to lift her in the air but Casper is still in front of her and holding her arms stretched out in front of her. He should have been above her head and her arms stretched out above her.
Casper tells Kat that he can't hurt her, and then makes his hand go though hers to show that ghosts cannot touch living beings. Yet multiple times ghosts touch people. However, Casper hesitates before answering (notice how quickly he says that she can't hurt him), and shortly after grabs Kat to drag her out the window. Casper knows that ghosts can touch people, and may not want to scare Kat away by admitting it.
When Kat is on the moving chair, her mouth gets covered in toothpaste. In the next shot, it's gone. However, she may have simply wiped the toothpaste off.
When Dibbs is trying to break into the treasure box, He's using the crowbar backwards. He should be pulling the other direction. However, Dibbs is shown to be a somewhat incompetent lackey, so likely doesn't know how to use a crowbar.
Kat Harvey is registered at school as Kathleen. But earlier, the news anchor referred to her as Kathy. Both Kat and Kathy are legitimate diminutives of Kathleen. Kat is likely changing her short name as she gets older.
When Carrigan slips on the brown substance in the hallway, she starts slipping before she actually steps on the stuff.
Casper's reflection is not visible in the mirror. Neither is Kat's, even though she is right next to him.
When Dr. Harvey rolls down the stairs, he gets wrapped in the carpet on the stairs. When he gets to the bottom of the stairs he keeps rolling, and the carpet unrolls itself onto the floor. He going in the wrong direction for that to happen.
Slits in the door where the swords will come through are visible while Dr. Harvey is being chased by Stinky, Stretch, and Fatso.
During the Ghostbusters Dan Aykroyd cameo, you can see that the front tube of the Proton Pack (where normally the energy beams come out) is broken off, and just dangling around.
When Dr. Harvey and Kat are under the breakfast table, watching the three ghosts, the green screen is reflected in Dr. Harvey's glasses.
When Carrigan and Dibs flee from Whipstaff during the storm, what appear to be the long sleeves of a red jacket are clearly visible draped over a large concrete flower pot to the right of the front door. Carrigan and Dibs drive away, and right after their SUV exits the frame, we see that the red jacket is gone. We can also see that this was a single shot without a cut, meaning that somebody had to be on the porch, out of sight, and able to remove the jacket in the two seconds it took the SUV to pass in front of the flower pot.
Despite apparently being condemned, Whipstaff Manor is in relatively good condition; its only major problems are cobwebs and faded paint.
When people die and have unfinished business they become a ghost until the unfinished business is done. If Caspers father had the unfinished business of resurrecting his son, why didn't he stay behind as a ghost?
Casper thinks he is made of the tingly feeling from your foot falling asleep. However, he has no memory of being alive, and by extension no memory of having feet, and as such should not know about that feeling.