The part in Violet's hair switches sides several times. This was deliberately done by the animators to aid the ease of animation, as long hair was something that had not yet been attempted.
When Mr. Incredible fights the first Omnidroid and he is injured on his left shoulder (and his suit is torn), his injury disappears and reappears several times between shots.
When Syndrome introduces himself to the public, he does so by catching a petrol tanker, which he then flamboyantly tosses behind him and we see a huge explosion. Barely a second later, when the Omnidroid is creeping up on Syndrome, he looks over his shoulder and we briefly see the street behind him, which has no trace of the tanker, or any fiery debris.
Before the wedding scene, Mr. Incredible summons his jet car. When he opens the car door, the window is up. In the next shot of him, the window is down.
The position of the aftershave bottle by Frozone's mirror changes.
When Mr. Incredible is exercising by lifting railroad cars, the trucks (wheel sets) on each car stay attached when he lifts the cars off the ground. On real railroad cars the wheel sets are held in place by gravity, so if he lifts the cars, the wheel sets should stay on the ground.
During their wedding, Helen doesn't say "I do" after the minister says as long as they both shall live. For them both to be married, Helen has to make her vows which she clearly doesn't. This technically makes their marriage null & void.
At the end of the dinner fight the ceiling light is stationary, but when Dash opens the door for Lucius the light is swinging and Helen reaches up to stop it. That is because Dash zipped back to his seat after answering the door, and this caused the wind. This is not obvious without close inspection.
The world depicted in the movie has had a very different history than ours. Technology and culture are often much more advanced. Whatever chronology is given regarding music, technology, politics, design, etc., is "true" within the movie.
Kari tries to reassure Helen that she knows how to take care of babies, including assuring Helen that she'll have Jack-Jack listen to Mozart because studies allegedly show babies listening to Mozart are smarter. While a widely-held belief, it's a misunderstanding of a small study involving adults, and follow-up analysis has shown no correlation between listening to music and intelligence. It's completely in character for a teen trying to convince an adult to trust her, however.
Even though Bob was rightfully fired for severally injuring Mr Huph as well as causing severe damage to the offices, he should have been arrested for what he did as well. Bob actually committed crimes of bodily harm and vandalism. Bob really should have been remanded in custody till he stood trial. However, Rick Dicker persuaded Huph not to press charges.
When Syndrome says "You got me monologuing. I can't believe it", his jaw clips through his shoulder.
In the interviews portion, the first time Elastigirl is on screen, just as her sequence ends, she leans forward, and the curls on the lower end of her hair clip through her shoulders.
In the jewelry store after the fire, Frozone gets a drink of water by pulling the lever downward on the water cooler. While bringing the cup up to drink, the lever is still down, meaning there should be water still coming out of it.
As Mr. Incredible goes through the folder of the deceased Superheroes vs. Omnidroids, It is visibly clear that the same profile picture of the super heroine 'Psycwave' is used for the picture of the super heroine 'Vectress'. The same error is seen where the profile photo of the superhero 'Universal Man' is also used for the superhero 'Tradewind'.
During the last part of the interviews, when Elastigirl says "I don't think so," the curls on her hair clip through both of her shoulders.
When Bob is searching for the names of Supers in Syndrome's lair the keyboard shown contains a euro symbol which would not exist for another 40 or so years after the movie takes place (1962).
In Mr. Incredible's home office where he has different newspaper articles and magazine covers about him, the Newtropolis Tribune with the headline "Incredible Rescue At Sea" is dated September 14, 2002. The movie is set in 1962.
Though the movie is set in 1962, one of the cars shown is a Datsun 2000 Roadster, (identified by its grill), which was first sold in 1967.
The accident involving Stratogirl that Edna says happened in 1957 shows a 4-underwing-engine jetliner. The first of these, the Boeing 707, didn't enter service until 1958 and engines approaching the diameter of the ones shown weren't available until 1960.
Despite the majority of the movie taking place in 1962, Bob while living a 'normal' life is clearly seen using a computer at work and Dash's teacher uses a video tape to get Dash 'caught' for putting a tack on his chair. Computers never existed in the 1960s. In those days, office workers used typewriters for typing and ledgers were used to keep track of the accounts and finances before the invention of spreadsheets. Likewise, video tapes were not invented until the late 1970s.
The radio refers to a police chase on San Pablo Ave, but there is no San Pablo Ave anywhere on the "auto drive" navigation map.
Mr. Incredible saves people on an El train. It is later revealed that the family lives in the San Francisco Bay area. The El train does not state Bay Area Rapid Transit (BART) anywhere on the train.
When the Omnidroid attacks the city, Mr Incredible is able to defeat it in the same way he did it the first time, i.e. by having its claws pierce its body. However, Syndrome continuously updates the design of the Omnidroid based on the weaknesses exposed by the superheroes he forces to fight it, so it hardly seems logical that he never remedied such a critical design flaw.
When wearing her supersuit, Violet is able to turn completely invisible, including her orange headband. Her headband was not designed by Edna Mode, does not match her powers, and should be floating in the air every time she turns invisible.
Kari thanks Helen for calling a replacement sitter. This plot was originally meant to be in the film, but it was cut and released as a short film instead.
In the newspaper clippings denouncing superheroes, under the "Super Menace To Society" column, "innocent bystanders" is printed as "innocent by standards".
When Lucius and Bob are in the burning building, Lucius claims that "there is no water in this air!" In fact, water vapor is a product of combustion along with carbon dioxide. Therefore the air should have been full of water (vapor).
Helen believes she's alone on the plane, yet she changes into her uniform in the (undoubtedly cramped) lavatory. Why wouldn't she just change in the cabin?
While the Parr family is fighting the Omnidroid, Mr. Incredible tells Elastigirl to press the first button of the Omnidroid controller. After telling him to wait, she presses the last button instead the first one.
Kari states to Helen "Mozart makes babies smart." while holding a Mozart CD. Listening to Mozart or classical music does not enhance intelligence.