The nuclear-powered submarine USS Nautilus (SSN-571) is depicted as a fleet ballistic missile (FBM) submarine. However, the Nautilus was a torpedo-carrying attack submarine. Also, the Polaris FBM program was not operational until autumn 1960. Furthermore, the missile being fired is reminiscent of a UGM-73 Poseidon C3 missile, not fielded until 1972 on the Lafayette and James Madison-class SSBNs.
Dean is called a "Beatnik" during the film which is set in 1957. The term "Beatnik" was coined by Herb Caen of the San Francisco Chronicle on April 2, 1958 as a derogatory term, a reference to the Russian satellite Sputnik, which managed to suggest that the beats were (1) "way out there" and (2) pro-Communist.
Mansley says that the unidentified object entering Earth's atmosphere was assumed by some to be "a large meteor or downed satellite." In 1957 Sputnik was the only man-made satellite in orbit, so the idea of a "downed satellite" is premature.
When the giant robot hand crawls around in the house, at one part it's watching a Maypo commercial on TV; the one where Marky's uncle Ralphie swipes his cowboy hat. However, although this film is set in 1957, the mentioned commercial did not debut until the following year, 1958.
The stock of Hogarth's gun changes in appearance. When Marv Loach hands it to Kent Mansley, the "HOG" of "HOGARTH" is almost directly over the "HUG" of "HUGHES". When Kent looks at the gun in the car, the "HUG" has shifted the equivalent of two letters to the right.
When the jeep pulls up to shoot at the Iron Giant in the intersection, the ammo box on its machine gun is on the gun's right side. When the gunner shoots at the Iron Giant, the ammo box is on the gun's left side.
In the scene while Hogarth is talking to the Giant in the clearing shortly after bumping into the branch, it shows the Giants head without the dent, shows Hogarth, then shows the Giants head again this time with the dent.
When Annie's pickup is stopped by the soldiers, Dean says they need to get Hogarth to a hospital. At this point, Hogarth is still in the pickup. In the next shot, barely a few seconds later, he is already halfway down the street. Considering the speed he was running, he could not have got that far down the street in that amount of time.
The train that collides with the Giant's head is pulled by a Norfolk and Western Railroad locomotive. The N&W never operated in Maine. Also, the locomotive is a streamlined passenger type, which wouldn't be pulling a freight train.
When Hogarth leaves the house to encounter the giant for the first time, a crescent moon is shown touching the horizon. The TV station has not signed off, and the plot suggests it is a time when kids are in bed but adults are still up, so it has to be before midnight. However, the moon's crescent is to the left, which would indicate a waning moon rising in the east shortly before sunrise.
When the deer comes to the giant, the giant's finger appears proportionally bigger. The deer appears very small compared to the tip of the giant's index finger, considering the giant's whole hand was able to fit in the bathroom.
At the end of the movie, the Giant is seen as he "comes to life" again on a glacier in Iceland. The name of the glacier, typed in large letters across the screen, is misspelled "Langjoküll" instead of the correct "Langjökull".