Glitches

Pausing during wakeup
If the game is paused during wakeup, the character getting up from the floor automatically disappears. In VS mode, this would result in the character with higher health winning. In arcade mode, it results in a draw once time runs out. This glitch can be used to win entire games, as the player has priority in winning in arcade mode should there be two draws.

Multiple falldowns
It is unknown whether or not this was intentionally put in, but under certain conditions the losing character will fall down more than once. For example, if one loses by pausing the game while the other is knocked down, the glitch will occur.

Arcade mode draw dialogue
In arcade mode, if the result is a draw, the CPU sprite will show up but the game will proceed as normal. This glitch was acknowledged by 18kingyo, and is a limitation of the game engine that 13.5 runs on.

Akasaka 623 glitch
Under certain conditions, Akasaka's 623's upwards acceleration will not stop and he will go up much higher than intended, moving up more than Youmu's 214B. It is unknown what causes this and what advantages or disadvantages there are.

Combo counter glitch
A combo lasting over 99 attacks will not increase past 99; in fact, it does not even reset to 0. Instead, it loops back to 90 after reaching 100, and continues from there.

Mystia Infinite Glitch
When playing as Mystia, if you manage to get the enemy directly above the head with a j.236236A, and cancel it into a Last Word as soon as possible (Cancelling it later in the corner also works), you can put your opponent into permanent hitstun until you hit them. Hitting them once returns to normal, but if you hit them again while they are on the ground, they will start sliding towards you at a very high speed, stuck in permanent hitstun. Hitting them again with a projectile (or with a melee attack, should they be sliding towards you) will cause them to readjust direction towards the direction in which they were hit from--in other words, if they were hit from the right, they will start sliding rightwards. Amusement aside, you can proceed to combo them to death with feathers, melee attacks, or music notes.

http://www.mediafire.com/download.php?37k1rbx2bvgzk3m for an example.

Win Pose delay glitch
If you win a round, you can delay (or completely negate) going into a winning pose by pressing D or dashing before entering said pose.