I read a slightly different explanation for that, somewhere:
The script called for a body double to face away from the camera whenever both Kirks were on screen. The double's tunic would never need an insignia, so they didn't bother to sew one on. The trouble was, the show was still pretty new, and nobody noticed when Shatner was given the wrong shirt for certain scenes.
A much bigger continuity gaffe occurs in "Charlie X," when Kirk enters the elevator wearing his standard gold tunic and arrives on the bridge in his green wraparound.