At one point, a call can be heard for "Cadet Decker". This may refer to Willard Decker, who became captain of the U.S.S. Enterprise in Star Trek: The Motion Picture (1979) (played by Stephen Collins). Willard Decker is also the son of Matt Decker, who was mentioned as one of Starfleet's most decorated captains in Choose Your Pain (2017). Considering that Discovery takes place a decade before The Original Series, and therefore 18 years before The Motion Picture, the time line would be appropriate.
Stamets has to make 133 spore-drive jumps in a row. The writers originally chose an ever higher number: 525,600 as a reference to the song "Seasons of Love" from the musical Rent which starred Anthony Rapp. However, when that number seemed too much, they settled on 133 as an homage to 33 (2004) written by Star Trek veteran Ronald D. Moore.
Lt. Stamets mentions going to see La Bohème with Dr. Culber. Anthony Rapp and Wilson Cruz were in the musical RENT together on Broadway. RENT was based on La Bohème.
The mid-season finale of season 1. After this episode went live on CBS All Access, the series took a 6 week break, ostensibly to allow time for post-production work to be completed on the remaining batch of episodes.
When this episode aired on TV, the scenes with naked breasts had shadows placed over them.