The only odd thing is the emphasis on Riley and Kirk being eyewitnesses, especially since Kirk pulls up Kodos's photo easily from the computer. Lenore needed a motive to keep killing, though, and this is a way to establish survivors as a threat to her father, at least in her mind.
I think the significance is two-fold - 1. Yes, as you suggest, Lenore needs a motive to kill and these witnesses are a real or imagined threat to her, and 2.) The witnesses are the only people with a motive to do anything to Karidian - first Leighton, then Kirk and finally Riley are all pulled into this melodrama - the traumatic events of the past, no doubt, overshadowing their normal lives.
It makes sense, overall.
Kirk points out the "flight deck" where the shuttles are kept. I believe this is the first mention of shuttlecraft aboard the Enterprise.
This scene was interesting for several things - I believe you are correct that it is the first mention of shuttles in TOS. It is also the only time we see the observation deck in TOS and the only time the simulated "night time" is seen or referenced in TOS (contrast that to 10 Forward on TNG, which seemed to simulate evening all the time.)
Finally, it is the overt courtship between Kirk and a guest star with the greatest disparity of age (Lenore is 19, Kirk is ~35 during the episode). But that's not the truly unique part, the dialogue between the two, particularly Lenore's best line -
And this ship... All this power, surging and throbbing yet under control. Are you like that, Captain?
is the most aggressive pickup line used by anyone in TOS - and spoken by the youngest, reasonably possible female companion of Kirk (Miri in the immediate previous episode was likely about 15, but it was obvious it was treated as a schoolgirl crush, and Kirk used it to manipulate her, rather than seriously contemplate furthering the relationship).
I'm amazed they got that past the censors.
She almost immediately follows this up by saying:
Caesar of stars. Cleopatra... to worship him.
Kirk's dialogue ranged from cheesy to malevolent - it was a good balance, and yet another example of why Shatner was the best man for the job.
Shatner was really in his element in this episode - a true romantic lead, a driven investigator, a wiley schemer (leaving them stranded) and a dangerous opponent. He did appear obsessed and this almost got Riley (and himself) killed, due to lack of proper precautions.
This post was edited on 8/15 at 2:03 pm