According to William P. "
@Tallguy" Thomas, reversing the decal is exactly what was done for the shot used in "Mirror, Mirror."
From
http://www.trekplace.com/tosfxcatalog.html:
WNM Side RL (Mirror, Mirror) [1]
Eleven Foot Second Pilot
[...]
This shot was obviously filmed to be used as stock footage during the making of Where No Man Has Gone Before. Since only the starboard side of the eleven foot model had detail, the decals had to be reversed in order to show the “port” side. It was never used except here to show the crew falling into the Mirror Universe. Ironically it is a much cleaner shot of the ship. You can clearly see the spikes on the nacelles.
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The other instance off the top of my head when the ship was shown "orbiting to the left" is in "Shore Leave." In that case, it was obviously accomplished by use of the mirror-image of usual stock footage of the ship orbiting a planet "to the right." In these cases, the letter/number decals couldn't be made out (at least, not clearly).
I can't swear that there weren't other instances of reversed footage.