There are two details in the trailer that caught my eye.
1. The pebbles starting to float just before Superman is launching.
This suggests they're going for the John Byrne version of explaining his flight (or they're at least using it as visual reference), where Superman has a way (probably an organ inside his body which has developed on earth) of controlling gravitons, in other words, he has the ability to manipulate gravity to some extent.
Chest hair sticking out of neck line. Oops.