The coroner tries to explain to Agent Dales how Dales' partner might have died. He says they will have to wait for the TOXOLOGY REPORT. Toxology is the study of archery. He should have said, "TOXICOLOGY REPORT"
The series mentions The House Un-American Activities Committee (HUAC) and then shows a newsreel from that committee, but the newsreel is actually from Joseph McCarthy and the Senate's Permanent Subcommittee on Investigations with Roy M. Cohn, not HUAC.
Roy Cohn is depicted as a tall man evidently in his 40s. In 1952, Roy M. Cohn was 25 years old, and he was 5'9".
Mulder is seen to be wearing a wedding ring, which is never explained in the context of the show. At the time when this scenes took place Mulder was with Diana Fowley, who helped him to discover the X Files, so it's possible that they get married for a while. This could fit together with the dark past that seems to be between them. In any case, the ring is also an inside joke in reference to David Duchovny's marriage to Téa Leoni, which happened in close proximity to filming.
The record player 'DUAL 1214' in the 1952 sequence was not produced before the late 1960s.
When Dales meets Hoover in 1952, there's a 50 star US flag in the room. That flag was introduced in 1960.
Michel mentions the "Chevy Chase PD". Chevy Chase has no police force, since it is not an incorporated entity. Chevy Chase is patrolled by the Montgomery County Police instead.