When Louis Reed (Mark Ruffalo) says that he 'gets' a student's T-shirt during a lecture, the shirt has a picture of Nicolas Cage, but the name John Travolta under it. This is a reference to the John Woo film Face/Off (1997) in which the two actors played each other's characters. Cage and Ruffalo also had collaborated on Woo's Windtalkers (2002).
Catherine Keener (Maya Sorian) plays both her younger and older selves through the use of deepfake technology as opposed to CGI de-aging, which typically is used in big-budget movies/series.
Jennifer Garner's golden retriever Birdy makes a cameo appearance. Hawking is actually played by a six-year-old female Golden Retriever named Marilyn.
A bullet wound, whether transfixing or not, through the abdomen, making "fart noises" when coughing reveals an obvious digestive tract perforation which will lead to infection, sepsis and death if not tended to by a qualified surgeon.