What I don't get is why Kodos didn't simply change his appearance with plastic surgery, especially since there was more than just 9 eyewitnesses still running around.
It appears that the identity of Kodos is not really in question: not only does Starfleet have complete records of his visual appearance and his voice, but there were 4,000 survivors of the massacre who would have that same information, and more.
However, that doesn't help any if Kodos goes missing. Where to look for him? In order to make an educated guess on that, one would need to know
who Kodos
was. Who was this mystery man who took the
nom de guerre Kodos, "The Law", took over the colony, and invoked martial law there? And that's where the son of a starship officer and eight other youngsters (or at least Riley and Leighton were of Kirk's approximate age) could well come in: Kodos could have been a starfarer himself, and arrived with the eight, who would thus have invaluable knowledge of his previous identity (or more probably his previous alias).
The nine were called "actual eyewitnesses who can identify Kodos". Is that an intersection of two groups: eyewitnesses (to the actual crimes), and those who can identify Kodos? Clearly, the nine aren't merely surviving eyewitnesses, because few of them survive and the computer knows that; rather, it seems the nine were the only original eyewitnesses with the (additional?) ability to identify Kodos.
Enough of that, though: both of Kirk's command decisions are odd indeed. Unless we decide he's not particularly intent on uncovering the Kodos/Karidian connection (because that's a triviality - everybody now knows Karidian is Kodos, but nobody can prove it in front of a jury, and Kirk, the computer and Spock agree on that), but rather on laying a trap for him so that the ambiguities would be removed. In which case inviting him aboard is a good decision, because it only jeopardizes Kirk's own life, which Kirk doesn't value over the mission. It only goes sour when it turns out there's another potential bait aboard (now why didn't Kirk remember that outright?), and Kirk may well consider Riley's life expendable as well if it serves the mission.
As for Lenore's ability to track down Riley, well, she could charm the boots off the captain himself. Obtaining the whereabouts of Riley should be a breeze with "social skills" like that.
Timo Saloniemi