Violence BioShock Infinite is bloody. Most of the violence is perpetrated with guns, and there is some blood spatter when enemies are hit. Furthermore, BioShock Infinite allows you to kill foes with a rotating blade attached to your arm. These kills are shown close-up and are appropriately bloody.
Scary Imagery BioShock Infinite skirts away from horror almost entirely, with the exception of one level late in the game that takes place in an asylum. There is one intense jump scare in this sequence, as well as frightening ambiance.
Sex & Nudity There are references to sex made by minor characters, though mostly in slang (i.e. "Could use a good roll in the hay after this").
Strong Language There is standard adult language in each BioShock game. BioShock Infinite also contains racial and ethnic slurs towards Native Americans, Black people, and Chinese people.
Substance Use There are bottles of alcohol and cigarettes lying around in Columbia. The player is not encouraged to drink or smoke. Drinking alcohol raises your health and lowers your Salts (resources that determine your secondary attack power). Smoking cigarettes lowers your health and raises your Salts. The games take place in time periods when smoking was considered healthy, and tongue-in-cheek advertisements depict people (sometimes children) smoking cigarettes—the player is meant to understand that this is historical ignorance, but it is not explained textually.
Discrimination BioShock Infinite has serious issues with representation. It addresses inequality in the city of Columbia—Black people, Chinese people, Native Americans, and Irish people are treated as sub-human, subjected to racist caricatures, etc. The game represents this cultural attitude very explicitly, in ways that could be traumatizing to people of those groups, especially children. Despite this, the game is generally sympathetic to the oppressed groups up until the point where they revolt and the player must fight against them.
One of the locations the player explores is a museum dedicated to Comstock's "heroism" in the Battle of Wounded Knee and the Boxer Rebellion. The museum is full of racist caricatures of Native Americans and Chinese people, and the exhibits feed false history to the spectators. The game is intended for people who know that the in-game portrayal of these historical events is purposely falsified.