The complicated machine, "mirrors that don't seem to reflect properly," and the definition "dramatic advance" are clues to the TV show "Quantum Leap", the TV show about time traveler Samuel Beckett.
Each episode of the show opened with the date of the "leap." The month/year pairs and descriptions of professions therefore identify particular episodes. (One episode, "Lee Harvey Oswald," had more than one date, but only one was in October 1957. In the final episode, "Mirror Image," Sam does not leap into anyone, and seems to be himself.)
The episodes are:
Aug 8 1955: The Color of Truth (chauffeur) Oct 8 1956: Return of the Evil Leaper (college student/superhero) Apr 1 1976: Disco Inferno (stuntman) Nov 9 1957: Good Night, Dear Heart (coroner) Aug 5 1956: How the Tess Was Won (veterinarian) Oct 5 1957: Lee Harvey Oswald (Lee Harvey Oswald) Feb 6 1964: Blind Faith (pianist) Sep 1 1958: Rebel Without a Clue (biker) May 4 1985: Moments to Live (soap opera star) Aug 19 1968: Leap of Faith (priest) Oct 6 1957: Future Boy (sidekick) Oct 6 1979: Private Dancer (stripper) Jun 7 1958: Miss Deep South (beauty pageant contestant) Feb 2 1974: Thou Shalt Not... (rabbi) Nov 8 1965: Double Identity (Mafiosi) Apr 1 1969: M.I.A. (undercover cop) May 9 1974: The Great Spontini (magician) Sep 7 1953: A Single Drop of Rain (rainmaker) Aug 8 1953: Mirror Image (himself)
The episode titles are not relevant (nor are the names of the people he leaps into). Instead, taking the days of the episodes gives: 8 8 1 9 5 5; 6 1 4 19 6 6; 7 2 8 1 9 7 8. 8/8/1955, 6/14/1966, and 7/28/1978 were the three dates of the three-part episode about murder in Louisiana, and the title of those three episodes collectively is TRILOGY.