Since no-one else has mentioned it yet: there is a new(ish?) glitch called the Hazard Respawn Glitch.
Whenever you touch the ground (maybe after a jump only?) while having control of Mario, the game updates where Mario should respawn if he falls into a hazard. If you jump frame-perfectly upon landing each jump, this doesn't happen, instead respawning Mario in the center of each room. This so far has three known useful applications (two in all versions; one not useful in JP):
Prologue: Blooper skip
{video 1} {video 2} (2 frame-perfect inputs onto boat panel, where the respawn position also doesn't update. RTA viable)
Chapter 1: Bridge skip
{video} (~10 frame-perfect inputs into river; 1 frame perfect-input on respawn)
Non-JP: Ms Mowz skip
{video}
Other applications include a faster/easier West Rogueport Early (as in Ms Mowz skip, just go straight past both rooms), and TTYD room early (same, but Goombella buffer out of bounds and walk on the seam to the Pit pipe)
