List of Paper Mario: The Origami King glitches
This is a list of glitches in Paper Mario: The Origami King.
NOTE: All names are conjectural unless otherwise specified.
Autumn Mountain skip
At the tram station in Autumn Mountain, the player can clip between a wooden pole and the steps and jump out at a certain angle to land out of bounds on the other side of the fence behind the station. If the player walks around the corner, whilst staying close to the wall as to avoid the loading zone for the secret coin area, they can access the long grass field, skipping a small portion of the area.
Bob-omb duplication glitch
If the player manages to pull off the Autumn Mountain skip, they can duplicate Bob-omb. They will need to continue to the point where Bob-omb is knocked into Chestnut Valley, at which point they need to backtrack to the empty river, which will activate the cutscene where Bobby interacts with the boulder blocking the path. After this cutscene is over, they will have a glitched clone of him, and they can have both Bob-ombs in the party if they jump down to Chestnut Valley without activating the Paper Macho Goomba cutscene. When using this glitch, it is possible to bring the cloned Bob-omb into the Water Vellumental Shrine, though if the player enters the fight against the Water Vellumental with him, he will vanish from the party afterwards.
King Olly softlock
In the second phase of the final battle with King Olly, it's possible for the Thwomp to get stuck in mid air just above Mario. This prevents him from using the 1,000-Fold Arms or dying, and hence requires the player to reset the game to move on. 
Missing Origami Character in the museum
If an ally finishes a battle with an enemy that only appears in a scripted battle like a Black Shy Guy, that enemy won't appear in the Musée Champignon in the Origami Character section, keeping the player from completing the game 100%.
Professor Toad in the floor
In front of any tower in Scorching Sandpaper Desert, the player can get Professor Toad stuck in the ground by having him dig in front of the structure, moving back slightly and then speaking to Olivia.
Red house roof clip
By jumping at the right angle near some crates in Toad Town, the player will be able to climb onto the roof of one of the houses. From there they can wander along the tops of the nearby hedges, as well as make their way onto other rooftops in the area. 
In the Sea Tower, there is a moving pillar in the Earth Vellumental room that the player has to pull Olly Tape off of. However, in some instances, the pillar will not move after they do this, potentially rendering the save file unwinnable.
Sumo Bro glitch
Wave battle glitch
If a wave battle is supposed to start, but only one enemy is alive and another is in their death animation, it will still initiate a wave battle and consider both enemies alive.
As of patches, these glitches are impossible to perform.
Battle Lab Score Glitch
Missing Black Shy Guy Glitch
If the player lets Professor Toad defeat the Black Shy Guy enemy in the Temple of Shrooms, the enemy will not be registered to the museum as defeated, and they will be unable to face it again to register it. This glitch was fixed in version 1.0.1 by adding another Black Shy Guy to Scorching Sandpaper West, which can be battled as many times as the player likes.
MAX UP Heart Coffin Skip
In the Temple of Shrooms, it's possible to collect the MAX UP Heart in the coffin room by hitting it with the hammer while the coffin is closed. If the player does this, the Love Toad will not count the upgrade has having been collected, and will continue to say you need to find it.
This glitch has since been patched. The MAX UP Heart can't be collected without opening the coffin anymore, and any players who have collected it will now find that the Love Toad considers it to have been collected.
Rubber Band Freeze
Snif City Royal Hotel glitch
If the player turns off the water in the Snif City Royal Hotel, then doesn't free the Toad that the nearby Snifit was surfing on, they'll be unable to free it when they return later in the story. This makes it impossible to get 100% completion for Shroom City, and locks the player out of the secret ending. This glitch has since been patched.
VIP pass glitch
In Shangri-Spa, after obtaining the VIP pass to access the Spring of Rainbows, if the player leaves the path to the Spring of Rainbows after entering, the VIP pass will be gone from the menu. If the player then speaks to the Toad at the reception, they will not have the stamp card and there is no way to get another one. Saving after this point will brick the save file. This glitch has since been patched