Flashbacks of both Batman and Superman's regrets/mistakes
We see in the trailer that Batman has a shrine to Jason Todd (or Dick Grayson if you believe the leaks). I want to see a flashback of this, and also of how Superman killed Zod, which we also see makes a return in the movie. I want to see how these deaths affect each hero mentally.
Try to focus on the main three characters, and just set up Aquaman and Cyborg.
Now we haven't seen any footage of Cyborg or Aquaman yet, and I'd like it to stay that way. If you want to set up those characters in this movie than fine, but do just that. I don't want them being main characters in the story. Take time to craft Batman and Wonder Woman so that we actually feel for these characters.
MORE THAN ONE FIGHT BETWEEN BATMAN AND SUPERMAN
Obviously by the new trailer we know that there will be more than one CONFRONTATION between Batman and Superman, but I want there to be more than one fight. I want at least two. One where Batman gets utterly defeated, and maybe a couple mini ones where Batman tries out new tech before finally creating (or using if he has made it already) his mech armor.