I don't remember much of anything from the first part except for the Regen Gel and Stephen the Vulcan…
I remember the Second Part very well, but I had mistakenly thought it was from Haldeman's World Without End, but now that I look up the plot of that book I recall that I did read it and didn't think it was that memorable.
So I had read this before, I'd just forgotten all the "Crew getting to know each other and it's prickly" parts.
The Klingons enjoying the horrible neo-Shakespeare is like the good version of the endings of eighties cartoons where everybody laughed for two minutes.