The major problem is that there simply wasn't anything interesting about the villain, Apocalypse. I could get over the fact that he looked kinda lame, but other than that there just wasn't anything very compelling about him. One thing that has always been good about these films is that there were always conflicts between the good guys and bad guys where things went beyond just the physical and were downright personal. With Apocalypse, he basically just has a god complex, but his ill-defined powers pretty much justify them.
That said, all of the good guys were interesting, and it was cool to see the character arcs for Mystique and Magneto get carried through into this chapter. Sure, it's not doing exactly what the comic books did, but by this point they need to do things that make sense in context of the previous films and not force the characters into predetermined roles.
Speaking of making sense though, I probably should point out that by this point, the continuity of these films make absolutely no sense at all. There are things that happen in this film that flat-out contradict what happened in the previous films. I'm pretty sure that they don't even really care, and they figure that maybe the time travel hijinks of the last film can miraculously explain it all away. Whatever, that's not very important to me, but I know that it will bug some people.
Anyway, there were a lot of great moments and highlights of this film, but I don't want to give away too much. I'll just say what I knew going in but yet still managed to thoroughly enjoy. For one, Quicksilver comes back, and they do a super-speed scene that might very well rival the one from the last film. Wolverine gets a brief scene that essentially undoes the damage from his lousy origin film, and it's a good one. However, I have to wonder if everything leading up to that scene detracted from the main plot, and we could have given Apocalypse more motivation. We also get to see a bit of Phoenix, and that's always cool.
One thing that I also liked was how Alexandra Shipp was a big step up from Halle Berry as Storm. Berry is a fine actress, but I never really felt like she did very much for that part. Shipp managed to hold an accent, and I was slightly surprised to see that the actress is from Phoenix, Arizona. (I figured that they might have gotten an actual African to play her.)
Speaking of Storm, it should also be noted that the ladies definitely get a lot to do in this story. They get some of the biggest moments and they're some of the most powerful players. While I think that The Avengers franchise is better overall, Marvel Studios could take some notes from what's going on with the X-Men movies.
If you've generally enjoyed most of the X-Men movies so far, you're probably going to like this one just fine while not being blown away. If they've never done anything for you, or you've been overall pretty ambivalent about them, this one won't change your mind. Brian Singer has done a fine job with this franchise, but I'm personally pretty eager to see some new blood show us what they can do.