I came up with another one...
We should have had a scene in Broken Bow to drive home the roots of Archer's hatred of Vulcans (aka "show don't tell"). Here's why. The Vulcans are already a popular race with the fans and if we're going to understand why Archer hates and distrusts them...
I think we could have had a scene immediately after Archer learns he'll have Vulcan company for the BB mission.
We see a flashback to when he was a boy. We're "in the room" when Henry Archer dies. 12-year-old Jonny and his mother are present. Pages and pages of sketches of engines and formulae paper the walls of the room. A variety of engine models, come clearly abandoned before completion, sit on a work bench. After Henry is gone, Jon walks around the room, looking at his father's work, picking up the engines, imagining a space ship powered by his father's engine.
Soval arrives to pay his respects. Jon turns on him and screams at him to get out, it was his fault that Henry never saw his dream become real. He says he'll never forgive the Vulcans for what they did to his father.