I would've liked a scene on Earth with Shaw (and possibly Holloway) actively pitching to Weyland and/or Vickers, as was seen in the viral. But I also think there's power in the franchise having never really shown Earth up close. And I think a scene such as this could've worked too, but with that kind of longer, drawn out prelude (in addition to the sacrifice Engineer, David on the ship, the cave, etc) it would be even more of a different kind of movie altogether from the Alien franchise had it done so - and judging by the mixed response among fans, who knows how that would've gone.
I don't recall if the "jet ski" scene with Weyland and David was ever filmed. A lot of people would've probably hated it, but I would've liked to see that. The film seems to float between Blade Runner concepts (the synthetic person, the family neuroses therein, creation and free will) and the Alien standards.
Following on the Yutani thread from the viral, I would've perhaps made someone onboard (Ford?) a Yutani plant who goes snooping alone and suffers a terrible fate.