I actually didn't hate Bioshock Infinite for the story, but I was disappointed in it for other reasons. Mainly I don't like how they abandoned the immersion of exploring and rooting through a strange but familiar world in an open manner. They turned the game into an Halo experience, constantly moving forward, mowing down waves of faceless grunts with guns, moving from setpiece to setpiece with nothing else to observe or explore other than deliberate scripted events, and tossing around a few special abilities. Also, as much as they promoted Elizabeth and showcased some impressive stuff during last years E3, nearly none of that actually made it to the actual game. It was just as disillusioning as Aliens: Colonial Marines. Otherwise, I enjoyed the ride, even though it was just a ride. I wanted a Bioshock like in the original where you are an active part of the world around you, not observing it behind some glass walls and plot devices like in this one.
A lot of valid criticism I see on the story is in regards to continuity in the world. Especially since, in the games own rules, it makes no sense that vigors weren't commonplace among people even though they were commonplace in the world, and why scavenging is still around even though it serves no societal purpose, for example. The attempt at a mulitverse twist in the end actually doesn't follow continuity rules in the game's events (other articles detail and analyze it better than me). That ruffled a lot of people.