WARNING: This thread WILL contain unhidden spoilers for this entry. Because this re-watch is in a slightly-subjective chronological order and not in production order, please refrain from talking about the content of other episodes or movies in this thread. If you do, please put that content inside spoiler tags. Some people here may be watching Star Trek for the first time.
#3: Star Trek: The Original Series, season 1, episode 6 "Mudd's Women"
Written by Gene Roddenberry & Stephen Kandel, directed by Harvey Hart.
Stardates 1329.8 through 1330.1 (October 2266)
"You either believe in yourself... or you don't." - Captain James Kirk
While chasing down an unknown vessel that refuses to identify itself, the Enterprise suffers critical damage and is left on emergency power protecting the ship from being destroyed by meteors. While the ship is eventually destroyed, the Enterprise is able to save the people onboard; a boisterous man named Tom Walsh (Roger C. Carmel) and three very beautiful women. Captain Kirk finds out that Walsh's real name is Harcourt Fenton Mudd - a man with an extensive criminal record and charges Mudd with endangering his ship. But the condition the Enterprise has been left in forces them to rush to a nearby planet for replacement parts as Mudd & his women devise a scheme to seize control of the ship.
Originally released: 13 October 1966
"Mudd's Women" on Memory Alpha
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What did you think?

Thanks for taking this project on, OP. I love TOS, so you're doing the cosmos' work!
No idea what that "Kelvin" stuff is about, but I mostly stopped watching ST after the... 5th series, I guess ("Voyager"). I did kinda get in to a very recent one, with either Cpt. Pike or April, which seemed really good, but I believe it got cancelled early?
Appreciate your analysis, and pretty much agree. This series was trying to do things never quite seen before, so it's completely unsurprising that there would be some relative clunkers. That said, Carmel was brilliant as Mudd, and I'm so glad they kept him, as he went on to do the 'android' ep and even a TAS ep, far as I recall.