At one point during BioShock Infinite, you gain a vigor called Possession. The scene where this occurs is evocative and eerie, and the audio that plays at the time is partially to blame. If you play that eerie audio backwards, it becomes even creepier: you can understand what's being said. And this audio found by EveryClickCounts isn't the only secret audio in BioShock Infinite, either.
There is also secret background music. If you take an ambient sound in the game and you speed it up, it kind of sounds like a woman is singing. You can even make out a guitar-like tune, weirdly enough. IGN breaks it down:
Though these were the only two I could find, I wouldn't be surprised if there were other hidden audio things in BioShock Infinite. Feel free to share if you know of any others.
EDIT: Astute readers noticed that the backwards audio in the first video is actually a quote from Shakespeare. Romeo and Juliet, to be exact.
BioShock Infinite - Secret Background Music [IGN]
Secret Reversed Audio - BioShock Infinite [EveryClickCounts]