Starcraft – If I start a new StarCraft 2 campaign can I still watch the movies from the completed campaign

The campaign lists 26 total missions, though some of these are "A or B" missions. Though you may only complete one of these missions for credits / research / campaign credit, the other, alternate mission is available on the console on the bridge to be replayed any time you like for achievements, etc.

Given the nature of those "pick one" missions, I believe there are 29 total possible missions +- a bonus mission that is only unlocked during special circumstances. (Or there may be 26 missions +- the bonus mission, I'm unsure how the "Campaign progress" bar, x/26, accounts for the branching scenarios.)

Starting a new campaign does not erase achievements, unlocked portraits, or decals.

All it does is start the missions over, from the beginning, so you can, for instance, take the alternate routes on the 3 "choice" missions (and see the after-mission movies, which you aren't privy to when simply replaying the mission via the archive).

It may also be the only way to lower your elapsed time for the "Hurry Up it's Raid Night" achievement. (On account of being able to skip some missions)