Inexcusable how this feature was left out of the game. Do The Third some justice, and make a mod that lets us revisit any completed level/view any watched cutscene whenever we want to.
I've only spent a little time looking at how the game makes missions available, and... i really have no idea.
Anyway, it's a bit more complex than that, because missions alter the state of the game world, and presumably, we'd want to restore it at the end.
sr3_teleport_mission_start("m06", false)
mission_unlock( "m06" )
mission_set_next_mission( "m06" )