Congratulations for a very imaginative video! The idea of using physics to explain why Cinderella escaped the prince is original and has a lot of potential, and the production aspects of the video were very good! Some of the physics was also good (computing the speed needed to complete the run in less than 1 minute), but as I am an introductory physics teacher, I cannot help but offer some constructive criticism about some aspects of your story that could be improved.
1) To explain why it is not easy to sustain a long run with a big ballroom gown, it would be interesting to talk about air resistance, since it is not moving at a constant speed by itself that requires a force, but fighting against other forces that want to slow you down.
2) The equation F = mv^2/r (relating to a possible escape with the scarf) was a bit confusing, since it was not clear where the circular (or part-of-a-circle) motion would take place (by the way, you forgot the "2" in the formula). This equation might be eliminated altogether, because the fact that the scarf could not support Cinderella's weight was sufficient. (It is also not clear what you mean when you write "mass > scarf potential"... you probably wanted to say "weight (not mass) > maximum scarf tension".)
3) At the end of the video, you state that each time the prince stops he loses momentum, which is true, but it would have been more interesting to talk about the time needed to decelerate and accelerate again: that is the real reason why stopping costs time in the race.
I hope you don't find my comments to be too "nitpicky"... we physics teachers tend to be quite nitpicky when it comes to the concepts of physics! By the way, I thank you for your critique of part 3 of my trilogy of videos "This Is Physics". Like you, I'm having trouble getting other participants to give a community star-rating to my videos, so if you have watched my three videos and can leave a rating (using your author code) for each of them, it would be quite appreciated! (Feel free to leave comments and constructive criticism also!) I think many of the participants in the contest have not yet realized that a video NEEDS TO GET AT LEAST 10 COMMUNITY RATINGS to be considered for the final round, so I have started to actively ask for ratings... Don't hesitate to do the same, many authors had to resort to this approach in the previous contests organized by FQXi...
I hope your video does well in this contest. Good luck!