The documentary about Spock that is being filmed in this episode is a genuine title called For the Love of Spock (2016). In addition to clips from this episode being shown in the documentary, Jim Parsons, Bill Prady and Mayim Bialik were all interviewed for it.
Only acting credit for Adam Nimoy, son of the late Leonard Nimoy (who had featured in the show in The Transporter Malfunction (2012)). Adam has mostly worked as a copyright lawyer and a TV director, and has appeared as himself in a number of documentaries.
The clip from Star Trek (The Original Series) is from the episode "Where No Man Has Gone Before".
Wil Wheaton introduces Adam Nimoy to Sheldon. Wheaton is known for Star Trek: The Next Generation (1987), and Nimoy's first directorial efforts were two Next Generation episodes, Rascals (1992) and Timescape (1993). Ironically, Wheaton wasn't in either episode.