Loosely based on events of November 7, 2006, when multiple eyewitnesses at Chicago O'Hare International Airport (including control tower personnel and flight crews) reported an Unidentified Aerial Phenomenon (UAP) hovering over Gate C17.
Not a plot hole nor character error: After an hour into the movie, he wakes his teacher at her house to discuss his math problem. He cites SETI that the alien 1,420MHz signal is the same radiation frequency as neutral hydrogen, the most common element in the Universe. Helping attempt to solve for the remaining two variables she points out that aliens would not know what a meter is. The aliens would also not know other human measurement units, such as second nor megahertz (1 million oscillations per second). Regardless how you may measure things, megahertz and seconds are irrelevant units of measure, as the signal is equal to and the same radiation frequency as neutral hydrogen, thus establishing a new units of measure.
(at around 36 mins) When Lee questions Derek about the shape of the aliens, Derek jokes saying if they are "little gray men with big black eyes". It's a hint for the 1985 best-seller Communion, written by Whitley Strieber about a close encounters between Strieber with an alien race, depicted in the book as little gray men with a big black eyes. Eventually it was adapted to movie in Communion (1989).
(at around 1h 25 mins) In the credits, "First Woman in Space - Valentina Tereshkova" appears, an unexpected quote, but a fitting tribute to the Soviet cosmonaut.
(at around 41 mins) Trying to decode the message inside the static taped during UFO sighting, Derek mentions Natalie "Arecibo Message by Drake and Sagan". It refers astronomers Frank Drake and Carl Sagan, that on November 16, 1974 sent a radio message in frequency modulated radio waves using the antenna of Arecibo radio telescope in Puerto Rico, with destination the globular star cluster M13, distant about 25,000 light years from planet Earth.