Everyone who has a job on the wedding day. This is not optional and it is not a trust issue -- it's coordination. People do not read documents they were not given.
Distribute copies to: your wedding planner or coordinator, the venue coordinator, the photographer, the videographer, the DJ or band, the catering team lead, the MC (if separate from the DJ), the florist (for delivery windows), your officiant (for ceremony timing), and a trusted point person in the wedding party who can field questions from family.
Share it at least 72 hours before the wedding. Go through it on a call with your photographer, DJ, and caterer. The rehearsal dinner is a good time to walk the wedding party through the ceremony portion. A run of show that sits unread in someone's inbox until the morning of the wedding is not a run of show -- it's a document that made you feel better while you were writing it.
For events with formal check-in and guest management, Qzero's guest management tools handle RSVP tracking, on-the-day check-in, and badging - so the coordination layer underneath the run of show is covered, not improvised.