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Incorrectly regarded as goofs
Carl's cane always has four tennis balls on it even after he throws one or more of them to the dogs in multiple scenes. When Carl throws the ball to Dug, Dug brings the ball back to him. However, when he throws it at the pack of dogs later on, he doesn't get it returned. Hence the reason why he only has three tennis balls in the following scenes.
When the house first rises, breaking free of its foundation, the front porch is clearly empty. Yet Russell appears later in the far-right corner. This is explained by Russell later when he says he crawled under the porch chasing a "snipe." Apparently he hung on to something underneath the porch and crawled up later. In the short film George and A.J. (2009) it is revealed that Russell braced himself underneath Carl's house when it took off in the same way that Woody held onto Sid's milk crate when Sid picked it up in Toy Story (1995). However, in the Up movie several shots show the complete underside of the house as it flies off and Russell is clearly not there (or on the porch).
Carl's hearing aid appears and disappears throughout the movie.
The door to the house has a different number of outside door knobs through out the film. The number varies from 3 to 4.
When they are flying and Russell speaks of the cumulonimbus cloud, Frederickson turns his hearing aid off by turning the knob forward. When the lightning strikes, he turns it back on... by turning the knob forward.
The house's interior is actually quite larger than the exterior. In various scenes, it is shown that Carl and Ellie's chairs are placed in front of a bay window, which is not shown on the exterior of the home. It would have been located on the side opposite of the porch, but is not there. The only other bay window is at the front, where Carl stands to steer the house.
Kevin likes chocolate. In real life, birds get food poisoning from eating chocolate.
Carl releases the huge "bag" of helium balloons. Helium always wants to go up so with the volume of balloons, Carl would have had to store them underground in his backyard to keep that many hidden or else, the construction behind his house would also see them.
The construction foreman and his two associates are all wearing sunglasses in court, something a real judge would not allow.
It is never shown how the balloon canopy was ever created or if it was done in a single night. It would be impossible for Carl Fredricksen to have done it himself or even be able to tie it down since it has the obvious ability to pull the house from its foundations. There was no way that was depicted for Carl to know how many balloons were needed to be powerful enough to float his house, let alone lift it from its foundations. Also, there is no mention of where the numerous empty tanks of helium that appear in his yard came from.
The house stayed intact after being lifted up, despite being separated from its key structural support - the foundation.
There's also no way enough balloons would survive the storm they encounter to keep the house afloat.
The phrase "Jiminy Cricket" was used in common slang as a euphemism for "Jesus Christ" (in context of a "cuss" word) since the 1920s. The expression is spoken in movies like The Brave Little Tailor (1938) and The Wizard of Oz (1939). Pinocchio (1940) had a character named Jiminy Cricket who was named after the expression, not the other way around.
The age time-lines of the characters don't add up. When we see Carl as a child, Charles Muntz is a late middle aged man. But when they meet, they are about the same age. This is because the plot was slightly different in an earlier version of the movie. In that version, the birds' eggs would keep you alive for ever if you ate them, which is why Muntz was so interested in the bird, and the reason why he is still alive when Carl meets him. Pixar eventually decided to drop the concept about the eggs, but by then it was too late to change the part about Muntz still being alive and healthy. So they kept him in the final version and deliberately ignored that he should actually have been decades older than Carl.
Carl's house starts flying at the moment when he releases the balloons from the chimney; assuming that all balloons were already inflated and stored inside the house, this should have made the house float hours before already, regardless of whether they are inside or outside the house. However, it appears the balloons were in a giant sack in the backyard, and could have either been tethered down securely, or compressed to reduce lift.
Carl uses sails to propel and steer his house. While sails don't work if the balloon/house are moving at the same speed as the air mass, they do work whenever the wind changes speed or direction. The house has significant mass (weight) and so does not respond instantaneously to wind changes.
When Carl and Russell first stop the house from drifting off without them, Russell does not have his backpack and Carl does not have his cane. However, right before the house hits the ground, while they are waiting on the porch, Russell is wearing his backpack and Carl has his cane. Everything is scattered from the impact and Carl and Russell chase the house and stop it right before the cliff. They simply backtracked to reclaim their belongings.
When young Carl Fredricksen is running with his balloon in the hand and smashes at the tree, the tree's shadow is missing behind and only young Carl has his shadow as if he's floating in air.
Russell needs only 1 more badge to become a senior scout member but at the badge presentation ceremony, when it is announced that all members there are receiving a badge needed to be a senior member, we see that all the other members are missing many badges.
According to the commentary, there are fewer balloons on the house (which are also larger than usual) in some shots of the house from far away. This was done to make the individual balloons stand out more from a distance.
When young Carl breaks his arm, the ambulance he rides in has a modern electronic siren rather than a mechanical siren which an emergency vehicle of the 1930s would have used.
If Charles Muntz is so desperate to prove his skeleton of "the monster of Paradise Falls" is real, why does he eliminate anyone he thinks might be after the bird? If anyone, including the surveyor or the botanist, had found Kevin and proven she really existed, Muntz's bird skeleton would have, in turn, been proven to be genuine, rather than the fabrication of which he was accused.
Fredericksen needs a four-point cane to even walk, but when he is chased he can run in a sprint.