The one thing that piqued my interest of faulty was the time travelling. I mean even after the time paradoxes, I'm not quite sure that the turn of events would turn out just like how things did in the movie... but I'll let the X-Men fanatics figure out any discrepancies in that time sequence shebang. My friend also had similar thoughts on that aspect of this film, though the thing that bothered him was that the mutants that died would stay dead. I didn't share those sentiments, though.
Also making Kitty having time traveling related abilities seemed like a bit of a stretch, deus ex machina, or eucatastrophe (whichever you prefer). I had vaguely remembered that Kitty could phase through objects but my unfamiliarity threw me off when the movie threw that non-canon curveball for this movie's plot. This brings up how this X-Men film (since it's only the second X-Men movie I've seen for far) took it easy on viewers who don't necessarily have strong X-Men knowledge.
Besides X2: X-Men United that I watched in 2nd grade (back when I couldn't piece together movie plots even after watching movies several times) and the sparse X-Men cartoons from my childhood on Kids' WB TV, I went to watch this movie without all that much retained background knowledge on the mutants. Despite this I still made the plot of the film pretty well, since apparently Days of Future Past didn't rely that much on the previous movies.
Last but not least, (this isn't really a spoiler, since this scene isn't that essential to the plot) I want to mention the Pentagon kitchen scene with the teenage Quicksilver. The scene in a sentence is how Quicksilver hilariously disarms a group of Pentagon guards when the mutants are cornered in less than a fraction of a second (thanks to Quicksilver's speed). That scene was so funny and so well done. At first the comic scene seems a bit out of place in the overall serious movie plot... although after some reconsideration, it turns out to be much needed comic relief for a ominous plot that doesn't let up until the very last scene.
X-Men: Days of Future Past is a movie that doesn't disappoint. I'm definitely going to see the next X-Men movie. Oh, by the way, if you haven't watched the new X-Men film yet, you should be aware that there's some post-credits scene that hints at the next movie.