Part I: Lily
Part II: Nina
The character of Beth, played by Winona Ryder, is a minor but pivotal character in the film. She's the previous Swan Queen, and as we learn, the now-former paramour of the sleazy director. In the film, she's portrayed as bitter and frequently drunk after being replaced as the star of the ballet.
In the film, there's a sequence where the director presents Nina to the ballet's patrons, while attempting to make it appear that Beth is retiring gracefully. During this gathering, a drunken Beth confronts Nina outside, flat-out accusing her of sleeping with the director to get the part. (As we've already discussed, Nina doesn't sleep with the director to get the part, but she does sleep with him after getting it. She loses a little of the high ground there.) It's after this heated scene that Nina and the director go back to his place and he starts asking her about her sex life. (He claims it's important for the role.) The next morning, Nina is with the other dancers when the company gets the news that Beth was struck by a car and is hospitalized. The director thinks she did it on purpose.
In the script, the same plot points occur, but they are arranged differently. After a few scenes that make it clear that Beth's "retirement" is not by choice, Nina and the others get word of Beth's accident. The gala for the patrons is just a few scenes after that, and for the most part, it serves the same purpose as the scene in the film.
But the scene is much more engaging in the movie. Putting Beth in that scene adds an additional level of tension. Will she make a scene? Will she confront Nina and the director in public? Also, in the film, Nina is clearly very nervous at the gala. If an aggressive Beth comes after her there, will she be too fragile to keep it together. The confrontation itself also brings back the issue of what a sleaze the director is when it comes to his leading ladies, a fact that will become relevant in the very next scene.
Most of all, since we see just how distraught Beth is that night, it lends greater credence to the theory that she stepped into traffic on purpose. In the script, Beth's accident comes completely without warning, while the movie gets us thinking that this won't end well for Beth certainly by the time we see her come apart at the gala.
Another detail that might be of interest is that the creepy hospital scene where Beth appears to stab herself isn't in this draft of the script either. I don't think it affects the plot much one way or another - certainly not as much as the previous change - but it does make for a haunting image. In that respect, it's probably a change for the better.
From this, we can learn that even scenes that seem to be working fine can be improved, and how small changes can give them greater impact without making sweeping changes in the story.
Part IV: The Natalie Portman/Mila Kunis Sex Scene