During the first ant encounter, Dr Harold Medford tells the policemen to aim for its antennae, saying, "HE's helpless without them!" Later, he (correctly) explains that most ants are female, the rare males dying shortly after fertilizing the queen when a new nest is established.
When the FBI agent points out on the map where the first atomic bomb was tested, he indicates Southwest of Alamogordo near where White Sands Missile range is located. The Trinity Test Site is actually about 100 miles north of that region, far to the Northwest of Alamogordo.
When the police car with Sergeant Peterson, Agent Graham, and Doctors Medford and Medford, arrived at the trailer site, they are in the middle of a sandstorm. But the driver's window and the back seat window on the left side are rolled down. Even someone with no desert experience would roll the windows up in a sandstorm.
When Robert Graham shoots the ant that has Sgt. Peterson, he uses a rifle that looks like an M1 Garand, a very big bulky rifle. When he then turns and starts shooting at the other ants, he has a much smaller Thompson sub-machine gun.
When Pat and Robert spot the desert nest from the helicopter, several cars and what appear to be two buses or trucks can be seen parked on a dirt road behind the nest supposedly hidden in this isolated location, "in these hundreds of thousands of square miles of desert".
The first aerial shot of the ant nest, which is supposedly in the middle of empty desert, reveals not only a well-maintained road but at least 3 clean parked cars within a hundred feet of the as-yet undiscovered nest.
While the Army is searching the storm drains of Los Angeles for the new nest of giant ants, they are seen to be using radios for communication. Radios do not work underground - especially in reinforced concrete tunnels.
While in the helicopters, the Medfords talk on the radio as though it dual-directional, or like a telephone where you can both talk and listen at the same time. Aircraft radios are (at that time) mono-directional, which means you can talk or you can listen, but not both at the same time. That is the reason for saying "over" when you're done talking, to let the other side know they can talk. Also, not only is "Over and out" NOT a "rule", it's not correct, even though Hollywood misuses this phrase all the time, since "over" means over to you and "out" means done with conversation. The proper sign-off would be something like "search one out."
The telegram announces that Doctors Medford will travel aboard an Army plane. They arrive aboard a solid-nose, transport variant of the Mitchell B-25J which went into service in January 1944 with the US Army Air Forces. However, in 1947 (seven years prior to the making of Them!) Congress disestablished the USAAF and created the US Air Force. In fact, when the plane lands in the movie, you can read USAF on the underside of the wing, thus it was not an Army aircraft.
When entering the L.A. storm drains, Dr. Patricia Medford's Jeep registration number is 328928. When Sgt. Peterson radios to "Stop all motors" his Jeep registration number is 686593. When Medford's Jeep is seen again, the number has changed to 686593. Shortly after, Jeep number 686593 is seen again on the surface used by the soldiers entering the manhole. The registration numbers are like license plate numbers so they are unique to every Jeep.
When Peterson is investigating the sewer drains in LA, he reports that he has detected the same "brood odor" he smelled in the nest in New Mexico. But when he was in that nest he was wearing a gas mask to protect him from the cyanide gas they had used to kill the ants. He could hardly have detected a "brood odor."
Early on, while the cops investigate inside Gramp Johnson's Store, there is a lamp in the right-hand corner of the screen that is swinging due to strong desert winds. The string that is causing the swinging is clearly discernible.
The goof items below may give away important plot points.
After the ants attacked the crew of the S.S. Viking, we learned the ship was later sunk by gunfire from the Cruiser USS Milwaukee. The Milwaukee was transferred on loan to the Soviet Union in 1944 and returned to the U.S. in 1949. A month after it's return the Milwaukee was decommissioned. On 10 December 1949 the ship was sold for scrap.
When the ants burst through the wall of the first (naturally excavated) nest and Sergeant Peterson retaliates with a flame thrower, man-made wooden support beams can briefly be seen behind them. This is because this is footage taken from later in the film when the ants are flamed in the Los Angeles sewers.
The ants are destroyed in the original nest using cyanide (HCN) gas. HCN works by attacking hemoglobin and changing it into cyanohemaglobin, which holds tightly to oxygen and won't release it to tissues. As Dr. Medford points out, ants and other insects breath through spiracles in their sides, which send oxygen directly to individual cells via tiny Malphigian tubes. Insects have no hemoglobin, so they would be immune to HCN. Something like nerve gas would work because it is similar to organophosphate insecticide.
When the helicopters find the nest, an ant comes out with an intact human rib cage and drops it to roll down next to Ed Blackburn's skull and equipment. The bones are stripped bare, which might be possible with normal-size ants, but not with giant ants, who would be too big to get all the flesh off the bones or even to get neatly between the ribs without breaking any of them. Also, only Blackburn's bones are found. No trace of the missing (and presumed dead) FBI family are found.