As far as I can gather, the original plan in Bob Justman's mind--and apparently GR's as well--was that all starship personnel, regardless of ship, would wear the arrowhead. This would mirror the concept that all Starfleet Command personnel would wear the starburst pendant, which was (more or less—just who was that ensign outside Mendez’ office?) faithfully adhered to throughout the series.
It appears that Bill Theiss later disregarded this construct, even though he had followed it on "Court Martial*." When it came time to costume William Windom for “The Doomsday Machine,” he designed a new patch to represent the starship Constellation. By doing this, Theiss clearly conveyed to the viewing audience—which included casual fans not fully in tune with all these ‘details’—that the character was not a member of the Enterprise crew.
He later repeated this decision by designing and costuming Morgan Woodward with yet another patch intended to represent the starship Exeter. After viewing dailies from the first day of "The Omega Glory" shooting, the infamous “under penalty of death!” memo was sent by Justman. By then, it was too late—there was no way Paramount would approve reshooting scenes to correct what they would consider a trivial matter—and so the Exeter patch stayed.
Let unexplained for all these years is why Justman or GR never caught the (apparent) costuming error on Windom’s costume months earlier. Maybe Gene Coon was the only one watching dailies that week?
Also left unexplained is just where Commodore Wesley, in command of the starship Lexington during “The Ultimate Computer,” was permanently assigned. This episode was shot before “The Omega Glory,” so the Justman memo hadn’t yet come into being. Was Wesley assigned to Starfleet Command and specially put in command of the Lexington only for that mission? Or did Theiss have a brain cramp and simply use the starburst to represent the Lexington’s patch?
I guess we’ll never know the real reason behind these inconsistencies, and so we’ll continue to burn many brain cells trying to deduce some plausible answers.
In any case, it would appear that the original concept was back in place for season three’s “The Tholien Web.” Several (deceased) members of the starship Defiant’s crew are clearly wearing the arrowhead patch… and yet, it’s obvious from the placement of bodies, restraining straps, etc., that the patches , while clearly present, were covered up in many instances. Why????
* From personal experience, I can understand why Theiss would want to change this; it was very confusing for me to try to figure out who the hell “Timothy” and his cohorts were. Since they wore the arrowhead, I initially made the assumption they were part of the Enterprise crew. For years I couldn't figure out why (what seemed to be) members of Kirk's own crew were badmouthing him at the bar (and getting away with it!). I also couldn’t understand why Kirk was saying he hadn't seen them in years. Don’t get off the bridge much, captain?
