Been awhile, but it may be a good idea to add some of my knowledge here if anyone else wants to run this cursed game haha.
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When jumping, let go of the direction you are going to lose less speed while mid air.
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The capes flying mechanics are a tad odd. If you don't do a full height flight by bumping your head or if something else stops you early, the flight height for the next jump will be effected. 7min 5 sec to 7 min 40 sec shows it off. This effect will also transition levels which can be useful if you know ahead of time.
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More with the cape. You can fly with less room if you keep switching power ups while holding a direction.
If you only have 1 power up you can also pause the game, but have to alternate directions in order to fly off of small platforms. This can be seen 28min 15 secs into the video.
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You can super jump with Yoshi. Even though it is not shown in the video if you time it just right while having a cape on, Yoshi can jump very high.
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Yoshi+Water is fast. Again not shown in the video, but if you get close to the kill plane with Yoshi while in the water, you gain a nice speed boost. You must also hit him in the head and jump or you will die.
It it a very hard trick (why I wasn't using it) but can save time if you do the other trick with Yoshi's super jump while making your way to the water level.
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Reznor can be damaged while being Super Mario. Just need the correct angle to hurt them without getting damaged yourself. 16min and 18 seconds in you can see this being done
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(Unknown Cause) Checkpoint warp after completing castle 3-4 to level 4-1. After completing 3-4 you can start level 4-1 at the midway checkpoint. I am not 100% sure what causes this, but I think it happens if you take the mushroom at the boss door on the same frame you enter the room.
This is most of the useful stuff I can remember about the game. Sure it will come in handy for someone that wants to speedrun this game.