List of New Super Mario Bros. U / New Super Luigi U glitches
From the Super Mario Wiki
Double Iggy Shell
This glitch can be done in Iggy's Volcanic Castle. When Iggy Koopa is on the top roof, once he falls off it, Mario must immediately jump on him. He then goes into his shell, but another one appears and be faced sideways. The glitch ends after a few seconds.
Nabbit Chase Glitch
This glitch happens during the Nabbit chases, where the player has to chase Nabbit and grab him while above a pit. Even though the player has caught Nabbit, the game instead thinks that he escaped and does not drop a P-Acorn upon returning to the world map.
This glitch only works in Boost Mode. When Kamek uses his magic in his boss fight to create blocks, the player has to put a Boost Block on top of him and jump below it. Kamek flies off the screen, making the battle unable to be beaten. This glitch works for almost any boss battle.
Stop the Time
The player should wait until the very end of the Time Limit on a Warp Pipe. If Mario enters the pipe exactly when the time changes from 001 to 000, he goes to the other side of it, and the timer remains stopped at 000 until the player touches the Goal Pole or exits the level. This goes the same for time Challenges on Challenge Mode. If one enters a door at the time where it turns from 001 to 000, they do not die as well.
No boss music
This only works on New Super Luigi U. The player should repeat the above glitch, but with a boss door. The player then has exactly 100 seconds to defeat the boss. However, no music is heard, although the boss' sound effects are kept.
Low timer sound plays twice
In New Super Luigi U, if the player hits a Mario Block for the first time in a play session (subsequently triggering the message describing the block's effects) before the "time warning" sound effect finishes playing, the sound effect starts over once the player has finished reading the message.