Comma placement in the newspaper. The sub-headline in H.I.'s stolen newspaper: "More than we can handle", laughs Dad. No editor at a paper, no matter how small, would miss the incorrect comma placement, which should be inside the quotes. It should say: "More than we can handle," laughs Dad.
In the aforementioned picnic scene, when Dot and Ed are talking, Dot is spreading mustard on the sandwiches; the mustard bottle's label is clearly blocked out (i.e. to avoid product placement). But, when she places the bottle back on the table, part of the label on the other side of the bottle is visible, clearly identifying it (to someone in the Midwest, or someone who has actually used that brand, anyway) as a Plochmann's bottle. They then switch to a shot of H.I., then back to Ed and Dot; the bottle has turned back to hide the label.
When Glen and Dot visit, everybody sits down for a picnic lunch. One of their kids (a little girl with her head wrapped in a bandage) starts throwing the green Jello salad on to H.I. But when they cut to the shot of Edwina and Dot, the Jello salad is in the middle of the table untouched.
In the picnic scene, where Dot and Ed are talking about the DIP/TET booster shots, Dot is squirting mustard on four pieces of bread. Yet when you see the bread a few camera shots later, the mustard squirts are different from the original designs Dot spread earlier.
In the Full Frame or Pan & Scan version, when H.I. is in the Arizona house kidnapping the baby, one of them "jumps" out of the crib and onto H.I. In the shot where the baby lands on him, a person's hands can clearly be seen at the top of the frame holding the child.
During the wild chase scene, H.I. commandeers a pick-up with driver. The vehicle shown is a 1964 to 1966 Chevy pick up. However, there are a couple scenes from inside the cab over the hood which clearly show the vents and contours of a Dodge pick-up of similar vintage.
The grocery store manager is clearly seen putting two shells in a double-barrel shotgun, but then fires at H.I. several times in rapid succession. (Intentionally done by filmmakers to illustrate how H.I. can never catch a break.)
The police take Nathan Arizona's fingerprints in order to separate his from those that the kidnapper may have left. Since Hi didn't use any gloves when he entered the quintuplets' room and since he has a criminal record (with his fingerprints on file), shouldn't the police learn his identity immediately through the fingerprints he left on the window sill and elsewhere?
The goof items below may give away important plot points.
When Nathan Arizona confronts the couple returning Nathan Jr, he puts his revolver in the crib to pick up the baby. Later on, he puts Nathan Jr. back in the crib but does not get his revolver back out of the crib.
After escaping from prison, Gale and Evelle steal a 1973-78 Ford station wagon (back-up lamps at the bottom of the taillights), but after the bank heist, they're driving a '71 or '72 (back-up lamps in the center of the taillights). After the dye pack explodes, there is a shot of the front of the car, and it's a '73.
When H.I. and Gale Snoats are fighting, considerable damage is done to the trailer. Gale throws H.I. into a gray cabinet by the front door, which cracks it. Gale then punches a hole into the cabinet. Later, when Leonard Smalls enters the trailer, the cabinet is intact.
As HI and Ed approach in their car for the final showdown with Leonard Smalls, shots of HI's face through the windshield show that the shift lever is up in the Park position, even though the car is moving. Since the background looks real, the car must be on a trailer.
When Gale and Evelle are in their getaway car and the paint bomb explodes in the car, Gale hits the brake to avoid getting in an accident, and later gets out of the car. He never put the car in park during this whole moment.