Since this movie is so well know most people will be able to identify the added material. It turns out he is their step-father and the youngest son is very ill. This adds scenes throughout most of the movie although it does little to advance the main plot. In the original he seems to get the number right away. In the special edition he has to search through several of her knick names until his father finally has him try under her married name.
Some scenes do help to flesh out the characters a bit more.
This helps to lay the groundwork for how David could come up with the computer virus needed at the end of the movie. There is also a scene specific commentary by the director and special effects supervisors. The second disc is full of extras. There is a half-hour making of documentary, a mockumentary of the invasion and a 33 minute HBO special on the film hosted by Goldblum. Add to this sotryboards, artwork and the unseen, unused original ending where Quaid attacks the ship with his biplane.