Each level's stars all have mild changes to the conditions of the level and the dialogue (you can't use the cannons while trying to obtain the first star of Bob-Omb Battlefield because there's a war going on, for example), but most levels are actually open enough to allow you to obtain most of their stars out of order (there's nothing to stop you from getting Bob-Omb Battlefield's sixth star by unleashing the Chain Chomp, and on top of that, you can use a glitch involving either a block or a Bob-Omb to clip through the cage with the star without freeing the Chomp, you can beat Mario Wings To The Sky without the Wing Cap, and you can reach the island without the cannon performing 2-3 precise long jumps from the mountaintop).
How is that even possible, you ask? By exploiting a bizarre glitch in the game called Cloning to create a road of floating, immovable Goombas.
He did a similar thing earlier by beating Mario Wings to the Sky, not only avoiding any A presses and avoiding using the Wing Cap to fly, but without even using the cannon.
note Though he has it held down all throughout the level, he never releases and presses it again - essential for standard jumps.
Famously, player pannenkoek2012 used the aforementioned Parallel Universe glitch to beat "Watch for Rolling Rocks" in Hazy Maze Cave by not only avoiding wall jumping to reach the star, but without even pressing the A button.
If not that, then you can use a tricky wall kick in the piano room (and the lobby too) to get to the second floor.
The BLJ also allows you to get to the upper floors of Big Boos Haunt without killing any Boos, which is extremely helpful for a Pacifist Run of the game.
A skilled BLJ also lets a player reach the "Elevator Tour in the Volcano" star without using the floating platform to reach it.
The BLJ and tool-assisting also allows a player to beat "Mario Wings to the Sky" without the Cannon or the Wing Cap.
There's another glitch that lets you bypass the Endless Stairs without the BLJ, but its a TAS-only trick that is impossible for humans to perform.
To make matters worse, its seemingly impossible to sequence break past the foyer key door - while the BLJ can technically bypass the door, the area leading upstairs will only load if the door is opened properly. Beating the game with 0 stars and 2 keys in real time has been achieved by several people however, it's pretty safe to say no-one will ever beat the game with only one key in real time. (This also saves time in ∻owser in the Fire Sea.) You can see the "1 key" TAS here. However, the game can think that Mario is above a floor even when his actual position is out of bounds, due to the way how the floor-checking variables loop. The game will not allow Mario to be in a location without a floor below him (levels such as Whomp's Fortress have an invisible floor below the death barrier, allowing Mario to jump above pits). note The (very simplified) technical reason for this has to do with the fact that the variables in memory for Mario's positions are truncated after exceeding a certain value when the game uses the variables to check if Mario is above a floor tile, and therefore in bounds.
You can skip the key for Bowser in the Dark World by using a combination of either the BLJ or the "Hyperspeed Walking" glitch with a "Parallel Universe" glitch, the latter being a glitch that allows Mario to access areas out of bounds.
It famously allows players to completely bypass Dire, Dire Docks, the Star Doors, and the Endless Stairs, and it also makes it so that the player can beat the entire game without collecting a single star! Unfortunately, this glitch was fixed in the DS remake, the Japanese Shindou edition re-release and the Super Mario 3D All-Stars version (which is based off the Shindou version). Since the game uses a negative number when you're moving backwards, this means that the small burst of speed you get when long jumping backwards in certain areas can just keep building and building with no way to stop it, meaning you can move at blinding speeds if you can do the right tricks. This is due to a discovery that Mario actually has no speed cap when moving backwards note The game has a speed ceiling as in, you can only go forward so fast, but there is no limit to how low it can go.
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The "Backwards Long Jump" glitch breaks the game wide open, since Mario can build up ludicrous speed and zip across the stage and through walls and doors in seconds.