I'm in a little too late to stop anyone accusing the game of being pretentious, but let me put it this way: The game is NOT pretentious, and if you think it is, then you don't know the meaning of pretentious.
It is quite self-serious, but self-serious != pretentious.
I disagree that the underlying themes of the story (racism, xenophobia, classism, religious zealotry) were shallow and artificial, but I will concede that I would have wanted them expanded upon and integrated further into the story, as they do have quite a tendency to be more "window dressing" than I'd have liked.
The story itself is fantastic. There's a real heart and soul to the relationship between Booker and Elizabeth, and while the side characters weren't developed as much as I would have desired, you tend to forget about them pretty quickly once the story moves past them.
The ending could have been framed better (it's a shame that the whole ten minute scene is basically non-interactive) but it conveys exactly as much information as we need to wrap up the story in the shortest span of time possible, and comes with some stunning revelations about who Booker is, who Elizabeth is, and why they matter so much.
The Aesthetics are the main unambiguous good of the game, with fantastic visuals of Columbia, and uncanny-yet-catchy anachronistic period music.
The gameplay is the main sticking point, and it's the aspect that most people get wrong, whether they liked it or not.
To put it simply, I agree a lot with Extra Credits, in that Bioshock Infinite's story outgrew its gameplay mechanics. Vigors make no sense: they hand out--freely!--a vigor that lets you control machines (and later people!); a vigor whose ONLY purpose could possibly be to mess with the well-established order of Columbia. A vigor handed out not 10 feet from an automated ticket-taker, the possession of which allows further access into the city! There's a thousand other ways that vigors stick out; this is only one of them.
I'm aware Jim Sterling had a video relatively recently (his episode spoofing Ludonarrative Dissonance) where he suggested that people unfairly criticized Bioshock Infinite's violence. You can reference that to see where I'm coming from in saying that no, they did NOT unfairly criticize Infinite's violence, they probably just couldn't properly articulate the real problems. There's a handful of specific moments where, yes, the extreme violence in Infinite was used to great narrative effect. But almost none of those moments occurred during actual combat. During combat, the violence rather invariably distracts from and undermines the narrative.
I'm not going to comment on the quality of the actual shooting mechanics, as I'm not a fan of the FPS genre and have no expertise on the subject.
This is about to get very long so here's the wrap-up: The Narrative+Story+Aesthetics are great, but everything about the gameplay works to undermine these otherwise fantastic elements. I'd still overall recommend the game solely for its story and themes, but it's not a 10/10 game