Alara Kitan was originally planned to have no eyebrows, so Halston Sage shaved her own off for the role. However the resulting look was received poorly, and for the remainder of the season she can be seen to be wearing false eyebrows.
Near the beginning of the series premiere, there is a scene that shows the bridge from the outside of the ship. This recalls the opening scene of The Cage (1966), the first Star Trek production ever filmed.
On the captain's desk in his ready room sits a model of the Wright Flyer, the plane used by Wilbur Wright and Orville Wright in 1903 for their first flight. Seth MacFarlane has stated that he chose the name "Orville" for his new show because he was reading a book on the brothers at the time, and realized that Orville, who is considered the 'lesser' Wright brother, would be a perfect name for the titular vessel.
The Epsilon 2 research center was filmed at the same building that served as the headquarters of the San Angeles Police Department in Demolition Man (1993).
The Institute is the same building used multiple times in Star Trek, mainly used as Starfleet Academy.