The front page of The Paper that Ron is reading has headline "Tragedy Feared On Space Station" with a photo of the Horizon space station from Space Race: Part I (2012) & Space Race: Part II (2012).
When Cyril complains about Archer shooting his pocket watch, Archer replies "Grover Cleveland called, he wants his watch back. He left two non-consecutive messages." Grover Cleveland is the only President in American history to serve two non-consecutive terms in office.
Cheryl mentions the Voight Kampff machine, a reference to the machine in Blade Runner (1982) & Blade Runner 2049 (2017), which is used to detect synthetic humans called Replicants. It worked by asking questions that are designed to elicit an emotional response, as only a real human has emotions.
When investigating the bullet that struck Brett for the sixth time, Archer calls it a "magic bullet" and references the Warren Commission, which investigated the assassination of John F. Kennedy.
Vanadium, the metal Krieger said he planned to use for Ray's endoskeleton, can be toxic to humans in several of its combined forms. Elemental vanadium is considered non-toxic.