Other mistake: The first setting was 2031 in post-apocalyptic Germany after a worldwide pandemic (an ongoing threat). Alexander met Joshua on August 27th. August temperatures in Germany are in the 70s-80s with a high probability of rain (which was absent). Both wore scarves and coats. The scarves were not being used to cover their noses/mouths to protect themselves from each other or whatever may have been in the air/atmosphere, so there wasn't a rational reason for them to be wearing either scarfs or coats. (00:10:30 - 00:11:18)
Other mistake: Water was scarce for some time, but the post-apocalyptic landscapes in most scenes showed numerous healthy-looking deciduous and evergreen trees with no signs of drought stress. Trees need to absorb many gallons of water per month to survive; the trees/forests shown were not distressed (or outright dead) like they should have been. (00:28:10)
Other mistake: Joshua kept on his thick leather gloves (with side stitching, adding width) while playing the piano yet didn't have any difficulty hitting the right keys. The added width to his fingers from this type of gloves should have interfered with his accuracy hitting the notes and keeping the tempo - the part of Chopin's "Nocturnes" he played was allegro (fast). (00:30:00 - 00:31:10)