Glitches (Super Mario Bros. 2J)
The glitches available to perform in SMB2J are very similar to those you are able to perform in the respective versions of SMB1 (NES/FDS and SNES), however their applications are slightly different. The pages here and here provide a comprehensive set of glitches possible in SMB1/2J, however this page focuses on glitches specifically relevant to speedrunning.
Correct Maze Answer Not Working
If Mario or Luigi is hit at the same time that they cross the checkpoint in the All-Stars version of Lost Levels, instead of hearing the ding signifying the correct answer, they will instead hear a buzz indicating the answer is wrong and the game will enact the wrong scenario. This is distinctly different than missing the queue by picking the right path and jumping over it, as you are very much on the right place for the ding to trigger.
Reducing Big Mario Hitbox
Small Fire Mario
Like in SMB1, Small Fire Mario is possible on the NES (FDS) release of SMB2J and not on the All-Stars remake of the game.
Spring Despawn Softlock
In the case of a spring despawn in the All-Stars version, such as in A-3, jumping where the spring normally is will result in a softlock. Mario or Luigi will be stuck in place with the player unable to jump to leave the spring. The player will have to either let the time run out or save and quit the game in order to advance.
Like SMB1, SMB2J features wall jumps which allow for advanced strategies in a multitude of categories. Wall jumps allow for the character (Mario or Luigi) to get a second jump off a precise point in the wall, allowing the player to reach places and make jumps impossible by normal means.
Doing a wall jump, while incredibly precise, is relatively simple to set up. With horizontal momentum, the player must land on a wall jump pixel (occurs once every 16 frames i.e. the size of a block), and on the same frame press jump. There are ways to set up the trick that allow for it to be done in a two frame window as the ability to clip into the wall is dependent on your horizontal subpixel as well.
This trick is possible with both Mario and Luigi and has a variety of uses in SMB2J including 1-2 (both as Mario and Luigi in Any%), 2-2, and 7-2.