Other mistake: When the kid first leaves and enters the house, he takes out the crossbow with an arrow in it but the elastic drawstring is flapping around in front. (00:22:33)
Factual error: Joel is using a ham radio set to contact his old colony. A shot of the radio set shows it is set to "CW", which is Morse Code, but he is using voice. And the strength meter is on zero. It should be showing the signal strength. (01:24:00)