20th Century Fox seems to regret the movie too, given that it allowed the many, many potshots against it in the promos for Deadpool.
Disowned Adaptation: Rob Liefeld says he and Jim Lee went to watch the film just to see the portrayal of Deadpool (which Liefeld created) and Gambit (which Lee created) and both of them were unhappy with what the movie did to their characters and Liefeld says he wrote a note to one of Fox's executives and wanted to reshoot the film with Deadpool having a mask but Fox executives scoffed him off.
The Fox executives decided that it would be a brilliant idea to take Deadpool, the Merc with the Mouth and possibly one of the most popular characters appearing in the movie, introduce him and then remove him quickly, and then sew his mouth shut. Because he would be too entertaining and take attention away from Wolverine or something (no-one knows the exact reason).
Director Gavin Hood and top Fox executive Tom Rothman reportedly had clashes over the film's creative direction. One infamous incident happened while Hood was off-set, at which point Rothman took it upon himself to have one of the sets repainted from Hood's original Darker and Edgier theme into something more Lighter and Softer.
Hood has also stated that the scripting process was a mess, and that portions of the screenplay were hastily rewritten as the movie was filming.
Fan Nickname: The version of Deadpool appearing in the film has gained a few, mostly related to how he is really nothing like the Deadpool from the comics. The most popular one appears to be DINO (DeadpoolIn-Name-Only). He is also referred to as "Dudepeel" by Imageboards, "Cesspool", "Barakapool" (because of the swords in the arms) and probably others.
Franchise Killer: The film was a brief Franchise Killer for the X-Men movies, since it was intended to take the franchise in a different direction following the original trilogy, but the terrible reaction to it killed these plans and a different (and much more successful) direction was chosen in the semi-reboot X-Men: First Class.
Missing Trailer Scene: One of the earliest trailers includes a brief shot of a young Black girl with white hair, who's clearly meant to be a young Storm. Her single scene was cut and can only be seen on the DVD.
Old Shame: Hugh Jackman isn't proud of the film, as he felt it did little justice to his character despite the high praise he received for his performance in an otherwise underwhelming movie; he helped make up for it with The Wolverine.
Promoted Fanboy: Will.i.am was a fan of the X-Men franchise who identified Nightcrawler as his favorite character and was subsequently cast to play a mutant with similar teleporting powers.
Stillborn Franchise: Played straight, but eventually subverted. This movie was intended to be the first installment of an X-Men Origins film series spun off from Fox's X-Men Film Series, to be followed by X-Men Origins: Magneto, X-Men Origins: Deadpool, and X-Men Origins: Gambit. After disappointing reviews for Wolverine, the Magneto script was eventually incorporated into the much better-received X-Men: First Class and the X-Men Origins series was scrapped. Years later, Fox would put resources into making Deadpool and Gambit movies, but without any actual connection to this film.
Troubled Production: The film was delayed by weather and Hugh Jackman's commitments with Australia, begun with an unfinished screenplay due to the writers strike — director Gavin Hood detailed that during shooting in Australia, script pages would be sent from LA, at times in the night prior to them being filmed; characters such as Gambit and Deadpool were also late additions — and saw director Gavin Hood entering conflicts with studio 20th Century Fox (along with the second unit who made action scenes too different from what he wanted), with Richard Donner (husband of producer Lauren Shuler Donner) being forced to join production to mellow out things. And an incomplete version with missing special effects leaked online one month before the film's premiere.
Dominic Monaghan was originally cast as Barnell Bohusk AKA Beak AKA Blackwing, but the character was changed to Bolt instead.
The cameos from Gambit, Cyclops and Emma Frost didn't happen in previous drafts, and the guy Logan went to see in New Orleans was actually Barbarus, an obscure Savage Land character from the comics.
Deadpool didn't appear either. The original final battle was going to be against a pack of feral, crazed Sabretooth clones. Presumably, this would've explained why Sabretooth doesn't speak and acts like a savage beast in the original X-Men movie, with the implication that the Sabretooth working for Magneto was actually just one of the surviving clones.