After Arnie climbs down from the water tower the first time, the policemen give him a warning and Arnie does the thing with his finger against his nose. His hand then jumps from his face, down to his side and back again between shots.
After Gilbert sees the husband on the trampoline outside, he puts on his jacket and he pulls down his apron, but when he's coming out of the house moments later, he pulls his apron out of his trousers.
At the end there is a tracking shot of the house burning down. In the foreground of this shot you will see the very same trampoline (with the red trim) that Ken Carver is jumping on earlier in the movie. In the filming process there was a scene where the Carvers give the trampoline to the Grapes which was edited out making it unclear to the audience why the trampoline is at the Grapes residence.
When the family go to find Arnie (after Gilbert hit him) they are at Becky's trailer. It is clearly very dark when they set out to find Arnie. In all the shots of Gilbert, the sky is dark, but in the shots of Arnie/Becky the sky is light as though it is dawn.
When Gilbert was driving the car to the police station so Mama could get Arnie the car was shown to be greatly leaning to the right indicating Mama's great weight, but when she got out at the police station the car doesn't rise.
While Becky and Gilbert are talking, she's wet up to her chest, but her hair is dry. When Gilbert walks into the water towards Becky, her hair is wet for just a moment, then in the next shot it's dry again.
In the shot where Gilbert chases Arnie outside after he is caught eating the cake in the refrigerator, the the sky is completely black, but when Gilbert carries Arnie upstairs and into the bathroom, the sky outside is a deep blue, suggesting the sun is still setting.
When Gilbert and Becky load her groceries in the rain they load them in the back of the truck under a tarp on the passenger side. When they arrive at the campsite they unload them from the driver's side.
When Gilbert first shows Becky his house, the sun is setting behind them. When the shot switches to show the house from their point of view, the sun is setting behind the house. Since they are facing the house, it is impossible for the sun to be behind both simultaneously.
When Gilbert first spots Arnie climbing the water tower, Betty Carver's house, the tower does not have any writing on it - it is plain silver. When their friend Bob arrives on the scene and looks up, the town name of Endora can be seen on it.
When Becky's grandmother is explaining to the mechanic about the worn needle valve, they are both at the back of the vehicle. When the shot opens up for the view of the water tower, she is talking over the shot, but she is on her own while the mechanic is rolling a tyre around the vehicle.
As Arnie climbs down from water tower for the first time in the movie, looking down on the crowd below, we see his sneaker fall and hit the ground. A few seconds later, it falls again and lands in front of Gilbert.
The goof items below may give away important plot points.
During the fire, Amy and Ellen are first standing well away from the house, back across the gravel driveway. Next they are sitting amidst the furniture in the yard, much closer to the house. Next we can see the back of the furniture but no Amy and Ellen.