When the Prof. is asked to invite the aliens to address the Earth at the United Nations, there is thunderous applause. When the film cuts to a stock image of the UN Assembly, no one is applauding.
When Jonathan uses Eve's radio after they get into a cab at the airport, she asks what type of music is being played. The radio plays big band jazz, but he tells her it's rock and roll.
The alien refers to worlds in many other "universes," but he obviously means other "solar systems."
If the weapon only killed those against the peace of the world, and after a high-pitched sound followed by death, why did Dr. Neuhaus die instantly in a flash of light and smoke? And, the Navy simply doesn't have television or telescope equipment able to sharply view something at a distance of 1501 miles.
When the doctor stands in the life raft waiting for the bomb to detonate, he stands perfectly still. If the raft was actually in the ocean, there would be movement.
The alien assumes that there are only two outcomes: humans use the weapons and destroy themselves, leaving Earth open for occupation OR humans don't use the weapons, and the alien species dies out, BUT there is a third, more likely outcome: the major powers use the capsules to attack each other (either pre-emptively or in retaliation) but millions of people in South America, Africa and Australia/Oceania remain alive (the five people chosen to control access to the weapons were all from the Northern hemisphere).
While there are places in the South Pacific, such as Point Nemo, that are more than 1500 miles from land, there would likely be ships within the capsule's 7 million square mile kill zone. There is a misconception that Neuhaus couldn't be delivered to the test point given the time course of the story. At full speed, a 1950's USN destroyer would take more than 5 days to get to Point Nemo from San Diego and another 2.5 days to get out of the kill zone. However, the dialogue is clear that the ship is about 1 mile outside of the kill zone, with Neuhaus just inside.
When one of the capsules is tested, Dr. Neuhaus instantly disappears. This would mean that every human within the 3,000-mile radius would have suffered the same fate. There would be no way of clearing everyone out of that size area anywhere on the populated areas of the Earth.