When Chambers is talking about the Kanamit's fertilizing process he says the soil had more vitamins than a drug store chain. While adding certain nutrients like minerals to soil would make it more fertile, vitamins would have absolutely no effect.
When Señor Valdes asks the Kanamit a question at the UN he is reading the question from a paper on his desk, face tilted down. When the camera angle switches to a close-up, his face is suddenly pointed up towards the Kanamit.
Chambers says that the new nitrate was demonstrated in Argentina, and that he knows the country was "barren and fruitless as any place on Earth." Argentina has the thickest layer of humus (fertile soil) in the world, and has always ranked among the largest world producers of wheat, soy and other grains, as well as fruits and vegetables, not to mention bovine cattle.
The Kanamit homeworld is described as "billions of miles" away. Michael Chambers notes that it's "100 billion miles off into space." But the Kanamits are from another galaxy. Traveling a hundred billion miles wouldn't even get you to the nearest star (Proxima Centauri), let alone another galaxy.
The TV station broadcasting the Kanamits' arrival at the United Nations building in New York has the call letters "JDQE-TV". TV stations in New York should have call signs that start with the letter "W".
In the beginning when Mr. Chambers asks the computer what time it is on Earth and is told twelve noon, he is asking a source aware of Earth's different time-zones, yet is given the answer of his own time, Eastern Standard time, since it is known that this is what he is referring to.
Chambers compares translating the Kanamit book into English to decoding Japanese messages in World War II. The two situations are entirely different. The codebreakers in World War II took a coded message, a meaningless string of Japanese characters, and reversed the coding process to produce a string of characters that would be meaningful to anyone who knew Japanese. Chambers's problem is not that the Kanamits coded their book, but that no one on Earth knows the Kanamit language. There is no way that they could take the book by itself and translate it.