I think the big problem of the story is that, in itself, Wolverine's mission in the past - stopping the assassination - is ridiculously easy. They know everything about who, when and where, they don't need to investigate anything, they don't need to look for Mystique because they know where she'll be, there's not really much obstacle or physical danger involved. Compared to say, the mission in The Terminator - to protect Sarah Connor from a terrifying killing machine - this is easy-peasy stuff. I've only read the synopsis of the original story, but from the memory it didn't spend all that much time on the actual stopping of the assassination.
So of course the movie then needs to manufacture obstacles in their way, which is why Magneto is brought into the story at all, first to have an obstacle of having to get him out of prison, and then to have him mess things up in Paris, and then to prevent the team from stopping Mystique at the White House too easily. Like, in X2 Magneto eventually turns on the team and tries to kill the humans, but he and Mystique are actually genuinely useful to the X-Men.
I think in the end my feelings about DoFP are not that dissimilar from my feelings about Star Trek: Into Darkness, in a way. Both movies are very much watchable because of the charismatic actors, engaging characters with good moments of interaction, they're fast-paced and fun. But good lord in heaven there are just soooooo many problems with the story, character motivations, recycling of the elements from the older movies, without the benefit of freshness of the previous film, that all of the good things listed above can only go this far.
