Throughout the final parts of the film, Jumba's head keeps switching from big to medium size to big again.
When Cobra Bubbles is at Nani's back door, the door swings to Nani's right when she opens it. But later when Nani crawls on top of the dryer and she opens it, it opens the opposite way.
When Lilo goes to dance class, the two drummers are playing the same kind of drum. When Lilo announces that Pudge controls the weather, one of the drummers has a different drum.
When Nani invite Cobra Bubbles into the house there is a pot simmering on the stove. She takes the lid off then turns around. After Lilo walks in, on the stove behind Nani and Cobra Bubbles the pot has turned into a frying pan.
When David sets the stage on fire, the hole on the canopy has a bamboo beam showing through. On the very next shot the beam is gone.
Stitch is dense, and therefore can't swim. He's the size of a small dog, and doesn't appear to weigh much more than one either; the six-year-old Lilo is able to lift him with minimal difficulty. Density is a function of both size and mass, so if he's able to pass for a dog in all respects, weight included, he should have the same approximate density as Lilo does.
When Stitch escapes in the police cruiser he lets out an audible horn. Sound cannot propagate in the vacuum of space.
Dogs should never eat or drink anything with caffeine in it. If Stitch wasn't an alien and was an actual Earth dog, Lilo would have probably unintentionally killed him for letting him drink coffee.
Spray bottles should only be used to stop bad behavior, such as chewing or jumping. Trying to teach a dog to play fetch by squirting it with a spray bottle is a good way to get a dog that doesn't enjoy playing and is afraid of you.
Tropical saltwater fish should not be fed peanut butter sandwiches.
Despite having been born and raised in Hawaii, Lilo speaks unaccented English, unlike her sister Nani who has a Hawaiian accent. There are several plausible "in-universe" explanations for this discrepancy (which are not mutually exclusive): Nani had spent a lot more time with her parents before they died, so she was more influenced by their accents than Lilo; Lilo has a lot of non-Hawaiian classmates as shown in the beginning of the movie (thereby being exposed to non-accented English), while Nani may have gone to an all-Hawaiian school; Lilo displays an unusually high interest in American movies and songs, particularly those of Elvis, and given her anti-social attitude it's reasonable that she's affected by this media a lot more than an average child.
After Stitch destroys the ships power grid at the beginning of the movie, one of the Gantu's deckhands checks on the computer to see if a police cruiser has been taken. Evidently, the computer terminal has a backup power, which allows it to keep working even if the main power is cut off.
When Stitch is first escaping the prison ship, the female pilot states that "He's loose on deck C!" and points at a moving red dot. However, the camera then shifts to Stitch, who is still locked in place. This is likely the result of the system being confused by Stitch spitting, so it thinks he's moving around, even though he's not, which produces a false tracking signal.
Myrtle the red-haired girl and the unnamed blond girl sometimes have noticeably lighter skin color than other girls, and in other times they are practically as dark as the others. For example, when Lilo runs to talk to the girls after class, Myrtle is nearly as dark as Lilo. This happens due to the difference in lighting conditions (granted, not very photo-realistically, but good enough for a cartoon). This is most apparent when the girls go out of a shadow into the brightly lit stage at the beginning of the movie. As Myrtle walks out of the shadow, her skin color becomes lighter.
When Lilo is running from the beach to dance class she is wearing a striped bathing suit, over which she puts on her grass skirt before entering the building. When she joins the other children on stage she is still wearing her grass skirt, but she is now wearing a tube top. Evidently, she pulled off her bathing suit from under the skirt (in a typical manner for small children) after entering the building, and put on the tube top.
Right before Stitch finds the Ugly Duckling book, he picks up three other books. The first two, "Oyster Farming: Is it for you?" and "Fire Eating for Fun and Profit" have their titles printed on the back of the books, and nothing printed on the fronts. This is needed so that the viewers could see the names clearly.
The license plate number "A113" shows up on no fewer than three different vehicles. This is an ongoing joke in Pixar films, but just the same, no two vehicles anywhere can have the same license plate number, as the plates serve the purpose of identifying an individual vehicle.
When Lilo takes her anger out on Mertle, she punches her glasses. Mertle's glasses do not have any damage after Lilo punches them. Mertle's glasses should have been broken or scratched.
In one of the trailers for this film, the aliens pronounce the planet Earth as "Earth". However, in the film, they pronounce it as "Ee-arth."