Yes, after the second pilot episode the science insignia and the ship services insignia were switched on the uniforms. That is why Scotty is wearing the science insignia in the second pilot episode and Astro-sciences physicist Sulu and Dr. Piper (and Dr. Dehner
) are wearing the ship services insignia in the second pilot episode.
I guess what I'm getting at is this: how do we know that the insignias mean "science" and "ship services" since they were used differently in the same series run? Example: Scotty goes from circular insignia in "WNMHGB" to reverse-C for many episodes and then sports the circular one again in "Lights of Zetar". And then the circular one again for more episodes. It doesn't sound like a mistake since the meaning of the insignia is not established and he had worn it previously.
Other ships (like the Constellation) don't appear to even have room on their insignia to differentiate between services (see Decker's insignia).
I understand what you are saying. However, during "The Lights of Zetar" episode, Scotty's insignia changes during that episode from the ship services insignia to the science insignia and back. I am not aware of any other time this happens to this character in another episode.
Yes, I agree with you that Commodore Decker's insignia should have a black star on it to designate it as a command insignia.
Navigator NCC-2120 USS Entente
Stokely: In an insane society, the sane man must appear insane.
Harvey Holroyd: Where'd you get that?
Stokely: Star Trek. [leaves the room]
Harvey Holroyd: [to himself] God, I miss that show. (Source: "Serial", 1980.