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Martin Landau essayed double roles in the pilot and "Wheels."
In "Shock" guest star James Daly played a kidnapped U.S. envoy, the enemy agent impersonating him and Dan Briggs disguised, thanks to Steven Hill's difficulties.
When Leonard Nimoy replaced Martin Landau as the disguise expert, he played his regular role of Paris and the Big Bad in "The Choice," and Paris, a double of a deceased premier and said premier (in pictures), plus the "Robot" of the title. There were also several times when he played minor roles in disguise and the audience had no idea it was him.
Creator Backlash: Paul Playdon, script consultant in seasons three and four, was so ashamed of his own "Time Bomb" (as were many who worked on the episode) that he actually left the show. (While he contributed "The Catafalque" in season five and has story credit on season six's "The Tram," he never returned as a staff member.)
The Danza: Subverted. Bruce Geller wrote Martin Landau's part with the actor in mind, going so far as to name the character "Martin Land" in the pilot script. Landau said he was honored, but requested the name be changed, which it was to "Rollin Hand". Played straight in "The Tram," with Victor French as Vic Hatcher (although even then it was nearly averted, as French replaced originally cast Keenan Wynn).
Defictionalization: According to the book The Complete Mission: Impossible Dossier the government contacted the producers to find out how they created a tiny hovercraft-like device that was (in show) controlled by remote control and sent down a shaft, somehow missing the somewhat obvious strings that were actually controlling the gizmo.
The self-destructing CDs seen in the 1980s revival series appear to act like DVDs - even though DVDs weren't introduced until the 1990s.
They were meant to be miniaturized laserdiscs (video discs that were read using laser like a CD, but were the size of a long-play record), which existed since the mid-80s.
In the episode "Robot" Leonard Nimoy plays his part under heavy make-up. This allows Paris to rip off his face mask in one take instead of the standard 'mask actor starts to take off face, cutaway to something else, cut back to IMF agent removing last bits of latex' routine.
At least in the first season, Martin Landau often played (with similar amounts of make-up) the people Rollin Hand was called on to impersonate.
Edited For F/X: When US cable channel F/X ran the series, bits with Briggs/Phelps giving counter-statements to agents in order to gain access to the recordings were removed, with the Tape Scenes beginning with Briggs or Phelps turning on the devices to hear the assignment. Other than that, episodes were presented edit free.
Fake Nationality: Israeli-born Nehemiah Persoff played the Big Bad three times: once as an Arabian, once as a Latin American, and once as an Eastern European.
The team adopt numerous ones in-universe, but the What the Hell Is That Accent?-worthy "Australian" one Paris puts on in "Chico" is notable because it's meant to be fake, as part of a persona which the week's Big Bad is supposed to unmask as fake, as part of the IM Force's plan.
Barbara Luna (from New York City) played a Latin American and an Asian in the original series, and a Latin American Big Bad in the revival.
Hilarious in Hindsight: In "Encore," William Shatner plays a 60-year-old gangster who's de-aged by the IMF for several hours. The show's idea of an old William Shatner is a bit at odds with how he really turned out...
Non-Singing Voice: Averted by Barbara Bain in "Illusion," Lesley Ann Warren (who had musical experience before [and after] her stint on the series) in "Flip Side," Greg Morris in "Blues" and Lynda Day George in "Trapped." And by Lynn Kellogg, an actual professional singer, in "The Martyr."
Possibly also Terry Markwell as the 1988 revival's Casey Randall whose character is killed off after only a dozen episodes.
Real-Life Relative: In the revival, Barney Collier's son Grant was played by Greg Morris's son Phil. Greg reprised his role as Barney in three episodes of the revival ("The Condemned" and "The Golden Serpent" parts 1 and 2).
Recycled Script: Done out of necessity in the revival series due to a writers' strike, but it was resolved early enough that only a handful of episodes ("The Killer," "The Legacy," "The Condemned" and "The System") were outright recycled from the original show.
Similarly Named Works: Both the original and the revival have an episode called "Submarine" - but unlike the episodes listed in Recycled Script above, the revival's "Submarine" is not a remake.
Technology Marches On: They went from tapes in the original 60s series to miniature compact discs in the 80s revivial. Likewise, in Jim's apartment, he uses a TV with a remote control to view the dossiers of agents and his table opens to reveal a computer with hard CD-type drives that were fancy for 1988. He wistfully goes, "Time does march on." The keyboard and remote then used to choose, then "accept" agents. Once Grant's selected, though, Jim has his team of four then, and another press of the remote finalizes them as "Mission Team."