When Lois opens the door for Peter's mom (she just left Peter's father) they stand in front of the open red door. When the camera cuts back to Peter, Lois, and his mother, the door disappears, leaving only the door-jam.
The Darth Vader cutaway gag implies that it is Vader who wanted to build the Death Star. This is very inaccurate, the Death Star was the brainchild of other Imperials, and Vader actually looked down upon it and had doubts in it.