During development, one religious developer threatened to quit because he was offended by the portrayal of Comstock, a Christian. Ken Levine decided to sit down with the developer and discuss the character; if the developer wasn't satisfied at the end of the conversation over what they would do with Comstock as a character, he would be allowed to leave with no hard feelings. In the end, the developer was happy with the changes Levine promised to give the character and returned to work, and the discussion encouraged Levine to write Comstock with more depth and personality than he had originally intended.
While Booker and Elizabeth walk through an arcade, she sees a game and remarks how she heard it was "delayed THREE times". This could be considered a sly wink from the writers, as Bioshock Infinite itself was delayed several times.
Albert Fink "created" his music by overhearing songs through the numerous random tears that would appear in Columbia. Because of this, the songs you hear being sung throughout the game are actually songs in the "future" re-worked to sound period specific. For example, the quartet in the beginning of the game sings "God Only Knows" originally by the Beach Boys and in a bar in the game you can overhear a version of "Tainted Love" by Gloria Jones.
While Booker and Elizabeth are walking through the streets just after she goes dancing, the tune to "Girls Just Wanna Have Fun" by Cyndi Lauper can be heard as played by street musicians; the song also turns up in its original version during one of Elizabeth's 'tears'.
Towards the beginning of the game, when Booker is baptized upon entering Columbia, before taking the baptism, a priest in a hall asks another priest: "Is it someone new?" This is a reference to the original Bioshock, where the first splicer the player encounters outside the bathysphere asks the same question.
In a tear opened by Elizabeth, there is a Parisian cinema projecting "La Revanche du Jedi", French for "Revenge of the Jedi", the working title of "Return of the Jedi". This tear probably gives access to a reality where the working title of the movie was retained.
In earlier builds of the game, Elizabeth had an array of psychokinetic powers that she would use in tandem with Booker's. In the final build of the game, Elizabeth's powers were limited to opening dimensional tears.
Many of the anachronistic songs in the game were arranged by Scott Bradlee, who would later form the band Postmodern Jukebox, which focuses on performing contemporary songs in various, often older, styles. He appears in the game as Albert Fink, brother of Jeremiah Fink. His dead body can be found in Emporia near a tear where Cyndi Lauper's original version of "Girls Just Want to Have Fun," can be heard.
In order to get an emotional performance from Courtnee Draper, Troy Baker and director Ken Levine repeatedly made derogatory and insulting remarks towards Courtnee Draper during recording sessions at her request, until she achieved the proper emotion necessary for the performance.
The Xbox 360 version of BioShock: Infinite became backwards compatible for Xbox One on December 13th, 2016. The BioShock games were some of the first announced to be coming to the backwards compatibility program. It took nearly a year for them to finally come to the program, and in that meantime a BioShock remaster collection was actually released for Xbox One and PlayStation 4.
When you get to Monument Island, before you rescue Elizabeth, there's a projector that plays several dates of Elizabeth being observed performing a variety of tasks. One of film clips is dated 04/15/12 which of course is the day the Titanic sank.
The trivia items below may give away important plot points.
At the end of the game, when Booker is confronted by multiple Elizabeths, one of the Elizabeths is the Beta model of the character seen in the first game-play footage. This may be a subtle inference that even the previously showcased version of BioShock Infinite (with different game mechanics and designs) is canon in another universe.
Towards the beginning of the game Booker is approached by the Lutece twins. One is wearing a chalkboard with a heads and tails column of which there are no tails recorded, only heads. They trow Booker a coin and tell him to pick either; he chooses heads. They mark the call, and as Robert Lutece turns around, you can see numerous other accounts of heads called on the other side, with zero tails. This hints to the fact that Booker is stuck in an Infinite loop, and shows that he has already been there before and has called heads repeatedly, creating an infinite loop of heads being called.
In the second tear Elizabeth opens, in Finkton Proper, where Booker is a revolutionary hero, you can hear a woman singing Creedence Clearwater Revival's "Fortunate Son," although neither Booker nor Elizabeth recognizes the song.