Factual error: When Sam speaks with his daughter on the long range phone there is virtually no delay between some questions and answers. It takes over two seconds for radio waves just to travel from the Moon to the Earth and back in a straight line. The interval between question and answer physically can't be shorter than that and realistically should be around 3 seconds or even more, accounting for additional signal relays and time needed for a person to form a statement.
Factual error: The Earth and the Moon are not in the same phase. The Earth is gibbous, while the Moon is crescent. In the real world, they should be in almost exactly the same phase from every angle of view. (00:01:50)