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.
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.
One of Hogarth's classmates calls him Pointdexter, most likely in reference to a character in Felix the Cat. The story takes place in 1957, three years before that character first appeared on the show.
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.
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. This commercial debuted the following year, 1958.
The steam locomotive which hits the Giant is a New York Central RR J3 class 'Hudson' locomotive. Some were streamlined for passenger service and normally never used on freight trains (especially in Maine, where the NYC RR never ran). They were all in scrap yards or having already been cut up by the time the movie takes place in 1957. None were saved.
When Kent Mansley meets Marv at the power station, he tells Marv his name is Kent Mansley. But after Kent's car gets stolen by the Giant, Marv asks "What are we looking at Mr. Manly?" Instead of Mansley.
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 Hogarth is talking to the Giant in the clearing shortly after bumping into the branch, it shows the Giant's head without the dent, shows Hogarth, then shows the Giant's head again this time with the dent.
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.
Dean's newspaper in the diner scene had an ad for BATTERY OPERATED MOON EXPLORER, which was a replica of the tin toy robots box front of the time. The same ad is mysteriously replaced by an ad for a lounge chair the next time the open newspaper page is shown.
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.
A US Army jeep pulls in and attacks the Iron Giant with a mounted M1919A4 .30 caliber machine gun. However, the one in the film is equipped with spade grips, while the actual M1919A4 would have had a single pistol grip.
Dean calls Hogarth after he just remembered that the giant was staying at his junk yard. It is unlikely Dean would have got the Hughes' phone number, if they just met only three days ago and had very little reason to know each other better in the interval.
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.
The goof items below may give away important plot points.
When the Giant saves the children and is standing in downtown Rockport, he appears to be barely taller than some of the tallest buildings downtown. But when Mansley sees him from the convoy, he appears to tower far over the buildings in town.
After the General gives Kent a dressing down for calling out the military just to see what he believes to be just some Beatnik's robot sculpture, Kent is seen sitting in the back of an army truck, looking dejected. Moments later, as the military convoy is driving away from Rockport MA, Kent is behind the wheel of a convertible automobile when he looks over his shoulder and sees the Giant towering over the town, slams on the breaks and causes the convoy to pile up.
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 scene before the Giant's rampage, one of the tank commanders says, "it's still alive". Notice behind him, another tank commander is doing the exact same thing. It's obvious that for time and budget, they copied the animation and shifted it behind him.