Blue House Skip gives Mario access to the area of the Toad Town Tunnels where the blue warp pipe to Chapter 5 is located. Under normal(casual) circumstances, Mario would need Sushie to reach this part of the sewer since her Field Action consists of maneuvering in water. Blue House Skip also gives Mario access to the Chapter 3 warp pipe without needing the Ultra Boots. To reach the Chapter 3 warp pipe, Mario simply needs to enter the Chapter 5 warp pipe, obtain Sushi, and use Sushi to reach the Chapter 3 warp pipe. Blue House Skip is utilized in every category except Glitchless.

Blue House Skip is the largest sequence break in the game and is also arguably the most difficult to learn trick. By performing Blue House Skip, Mario is able to perform a precise double jump and is then able to fall through the roof of the blue house. This gives Mario access to Chapter 5 much earlier than intended, and also skips a significant portion of the Chapter 5's beginning.

This allows a player to clip into the blue house. This would usually be done after getting Parakarry. It's probably one of the most difficult tricks to pull off. It requires jumping at precise timings onto the roof and going into the house early. Same idea as Lakilester clip (kinda).

This is basically the biggest game breaker found as of the date this was posted. Credit goes to Bonecrusher for the discovery and to r0bd0g for encouraging said discovery. This theoretically skips half of chapter 2, some of chapter 3, and all of chapter 4. Since the Yoshi/Raphael skip was discovered, Watt is no longer needed and neither is Chapter 4.

Both of the controller input videos below are courtesy of Sandsky0: Spin method, with controller input (aka sockfolder method) -- recommended:

BHS video by Peaches: