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, 2003. The movie is set in 1962.
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.
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 had been full of water (vapor).
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.
After Helen catches Bob coming home late from the fire and jewelry store incident, there is a figurine laying on the ground next to the blocks beside Helen's chair. The figurine disappears in the next shot.
As Bob gets chewed out in his cubicle by his boss, his pencil holder is centered on his desk. After the boss leaves, it has moved to the edge of his desk, where it falls off and spills pencils all over the floor.
Violet is not wearing the orange headband before the rocket launches but after it appears on her head. There is no way she could have possessed that headband as she was not seen holding it in her hand before the cave scene.
After the plane is blown up and Helen and the kids are in the water, Helen's hair is down below her shoulders. During the rest of the movie, her hair is shown as being short, only to her upper neck. Even wet, her hair would not be down below her shoulders.
When the airplane blows up and Dash, Violet and Helen are falling, once Helen makes herself into a parachute, there is no longer rubble from the plane falling around them and nothing above them. After they are in the water, a big chunk of plane falls almost on top of them.
After landing in the jewelry store, the rescued fire victims are strewn on the floor around the room. In the next few scenes, these people are no longer on the floor, but they reappear there when the cop draws his gun on them.
In Metroville, when the robot explodes on the water, the upper camera shows Frozone standing behind Helen and on the left side of Mr. Incredible. Then the same scene is shown from the front camera but now Frozone appears at the right side of Mr. Incredible and in front of the whole group.
In the Scene where 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 wheelsets should stay on the ground.
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's 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.
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.
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.
The goof item below may give away important plot points.
Bob drives his new black car to the airport for his second trip to Syndrome's island. Later, Helen drives her new red car to the airport to fly Snug's jet to the island. The family uses one of Syndrome's rockets to return to Municiburg, meaning both cars are still at the airport. Yet when the family returns home after defeating the Omnidroid, Helen's car is back in the driveway.
During the Jet sequence Helen has her travel bag during the missile attack then disappears after being destroyed by the missiles it is supposedly destroyed and she still doesn't have it when they are in the water then it suddenly appears when they are on the Elastigirl boat.