The Search for Spock, really only had one objective - to bring Leonard Nimoy back into the franchise. For the backstory, they chose to go with the same formula as for Khan - a fight over obtaining the Genesis device, but this time between Kirk and a Klingon captain. You would think from that description that the film was destined to be a dud, but several factors saved it and allowed it to hold up as a worthy sequel almost as good as its predecessor. First, there was continuity. The script flowed naturally from the prior film, with a returning cast save for Lt. Saavik, now played by Robin Curtis. At first that was disappointing because Kirsty Alley played such a great Saavik in Khan, but I soon realized that Curtis did a better job of portraying her as an emotionless Vulcan as would be expected. And James Horner also returned to do the score.
Secondly, Christopher Lloyd did a superb job as the villain Klingon Kruge. This was quite shocking to me. I've always loved Lloyd for his awesome comedic talent. I would not have expected him to do so well in such a completely different type of role, but he took it completely seriously. I did not even know it was him until the end credits. Finally, there were some big events that occurred to lend dramatic effect, like the crew turning against Starfleet, the death of Kirk's son, and the destruction of the Enterprise!
A character as central to Star Trek as Nimoy's could not be killed off easily. Likewise, it would not have worked to simply bring him back with the wave of some conjured up sci-fi excuse. Thanks to some foreknowledge, a few key scenes were added to Khan to allow a narrative to be built up for Spock's return that had some credibility (if not scientifically, at least within the arc of the story line). I think it was wise to bring him back slowly, with the culmination at the end of the film back on Spock's home world (it also probably helped to have Nimoy off screen for most of the film since he was directing). The final scene where Spock recognizes Kirk and begins to remember is especially heartwarming. They speak all the great lines that they did during the dramatic death scene, but in reverse order, and you realize that Kirk is taking him back from the edge of death to his old self again (see bottom). Also, the humor provided by McCoy having to deal with his annoying friend inside his own head is just classic. It was a good script, on par with the previous one.
The Search for Spock is probably my all time favorite classical soundtrack. Because he had more time (the Khan score had been written in 4 weeks), and he was basically embellishing upon music he had already written, he created an absolutely beautiful soundtrack. Just sit back and listen to the main title track.
I leave you with the transcript of Spock's death in Khan followed by the the end of Search. Remember that most of the quotes were set up earlier in the second Trek film and therefore are much more powerful when heard in context...
End of ST II:
Spock: Ship out of danger? Do not grieve, Admiral - it is logical: the needs of the many outweigh [Kirk: the needs of the few]....or the one. I never took the Kobayashi Maru test - until now. What do you think of my solution? I have been, and always will be, your friend. Live long, and propser.
End of ST III:
Spock: My father says you have been my friend. You came back for me. Why would you do this?
Kirk: Because the needs of the one... outweigh the needs of the many.
Spock: (as if remembering) I have been... and ever shall be... your friend.
Kirk: Yes.... Yes Spock...
Spock: The ship... Out of danger?
Kirk: You saved the ship Spock! You saved us all. Don't you remember?!
That last word - "remember" - was the word that Spock used to transfer his Katra to Bones and started the whole episode, and it provides the perfect end to the exchange.