I like this eps but for the really poor portrayal of Kirk.
His entire crew about to drop dead in six hours (!) and yeah, Kirk takes time to waltz and play billiards and ponder the oddities in Flint's collection and woo a woman. Really?
Even Spock and McCoy seem none too hurried about the critical medical emergency. Sure everyone speaks the words and counts down the hours, but no one acts like it's a life or death situation.
The thing of it is, the script invention of the Rigellian fever crisis aboard the Enterprise could have easily been changed. Instead of the Enterprise crew dying in six hours without ryetalin, make it a looming crisis in three weeks or three months on a nearby Earth colony when their ryetalin runs out.
Then you still have the medical crisis and ryetalin mission, but now I can buy Kirk's time investigating the mystery of Flint, his time with Rayna, and so on.