My favorite example of such a paradox is actually outside of Star Trek. Winston Groom, the author of the "Forrest Gump" novel, wrote a sequel after the Tom Hanks movie came out. One scene in the sequel novel has Forrest going to the Academy Awards -- where he meets Tom Hanks. (This scene might actually have been filmed if the sequel made it to the big screen -- except for the fact that Mr. Hanks doesn't like to make sequels as a general rule.)
Or the movie "Man on the Moon" where Jim Carrey played Andy Kaufman. In several scenes, he portrayed Kaufman as a cast member on "Taxi" alongside many of his real-life castmates, (Christopher Lloyd, Judd Hirsch, Marilu Henner, etc.) With the notable exception of Danny DeVito, who was also a Taxi castmember -- but was absent from that scene since DeVito played an entirely different character for the movie.
To keep it Trek-related, I recall reading a short story (author's name escapes me) where, due to a really bizarre transporter accident, Kirk, Spock and McCoy trade places with Shatner, Nimoy and Kelley. And the actors have to play their "real life" roles for a short time until the real Scotty figures out a way to send them back.