These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Bryan Singer's decision to ignore parts of X3 and Origins due to not being involved in them, and some comments he made about using this film to 'fix' these films problems. To some, is great news because of how despised those films are, while others feel this is him being an entitled egomaniac with no respect for other people's work. Being that this is the exact same thing, to a degree, he did for Superman Returns...
The decision to make Wolverine the main character of the storyline when Kitty Pryde was in the comics. It makes more sense with the movie series's established plotline(Wolverine is sent back via Mental Time Travel to the 1970's and Kitty hasn't been born yet) , but it's still a bitter pill for Kitty fans and people who wanted to see another X-Men movie where Wolverine was NOT the main character.
It's the Same, Now It Sucks: For a large number of people, the fact that the film is seemingly continuing the largely unfair treatment of Cyclops in favor of Wolverine. With Wolverine having his own movie, there's a good number of people who hoped he'd stay out of this one, and that Cyclops, and other characters who were unfairly pushed aside for Wolverine, would get a chance to shine. Instead, Wolverine's going to be in two films in the space of a year, and there's no confirmation on Cyclops, either as a young recruit or as his established adult self. Going even further, it would appear that the ''First Class' cast are being diminished in favor of the cast of the original trilogy.
Many fans are dreading hearing more about the movie, mostly because they're afraid that the return of the cast from the first three movies (specifically Wolverine) will overshadow First Class's mutants.
Wolverine being the one to travel back in time rather than Shadowcat, who did so in the original storyline. Part of the reason this causes backlash is that Shadowcat's role has been played by another character before, by Bishop in the 90's cartoon (presumably in an attempt to capitalize on the then-recently introduced character's popularity).