Another connect-the-dots is that Stephen Collins played Julie Andrews' husband on Broadway in Putting It Together, and Julie of course starred in The Sound of Music directed b y Robert Wise who directed ST-TMP.
I recall seeing Voyage Home at the Cinerama Dome with a very full audience and we laughed hysterically at the Mac mouse scene because, believe it or not, PCs were just starting to come into businesses (huge corporations I am sure had them sooner). I worked at a small medical practice at the time...