There is a wall glitch that the author used in Part 6. It can maybe be used to skip Bowser's castle and I'm investigating its usefulness apart from that now.
However, it only works in the Japanese version.
How it works: Have Mario use fire on Luigi and fall off a ledge. If done correctly, you can continue walking without having to wait for Mario to reach the ground. Now, while walking, Mario will be in a glitchy state which allows to enter walls by switching between Mario and Luigi.
Strangely, this timer problem is still present in the Japanese version:
http://www.youtube.com/watch?v=JzCe-kyNOJ4
Maybe it can not be used to skip Bowser's castle after all. I'm not sure how the author of the Nicovideo TAS did it.
I'm currently trying to retrieve the VBM file. If we can't retrieve the .VBM file, testing the glitch and verifying the Bowser castle skip will get a lot harder...
I actually experienced a similar glitch in the (E) version by chance while messing around in the final boss room at the throne, but I couldn't reproduce it. I confirmed that this glitch doesn't work in the (E) version.
Skipping much of the end of the game actually might defeat my idea of collecting mushrooms and using Mush badge since there are hardly any bosses left in the game now, so it won't be useful to use that strategy..
Video demonstration:
http://www.youtube.com/watch?v=r1u4167KfXc