After the over-indulgence of Star Trek: The Motion Picture almost sank the Star Trek franchise, it was the superbly (and cheaply!)-executed directness of Star Trek II: The Wrath of Khan that saved it. The hands-down best Star Trek movie gave the property a new lease of life and re-energised actors who were conflicted on continuing to appear in it in the future, most notably Leonard Nimoy, who had agreed to do The Wrath of Khan partially because it gave him the chance for a great death scene. Ironically, the experience of making the film was so good that Nimoy leapt at the chance to return, especially when he was also given the chance to direct.
Producer-writer Harve Bennett had a feeling during the making of The Wrath of Khan that the franchise would continue, so added a series of lines and shots setting up a sequel over director Nicholas Meyer's objections. The final cut included these against Meyer's wishes, leading to him refusing to have anything to do with the sequel; he and Bennett later reconciled, Meyer acknowledging it had been a good choice in the long run, but he was not around for this film. The script for the third film pretty much wrote itself from that point on: Spock is dead, but had transferred his katra or spirit into Dr. McCoy's mind just before the end. His dead body was then shot onto the surface of the newly-formed Genesis Planet, but since the Genesis Wave can bring life from lifelessness, the result was that Spock's body was regenerated as well. All that was required was a way to reunite the two, which was provided by Sarek (Spock's father) telling Kirk what had happened. Jeopardy was added from two directions: the Federation's refusal to allow anyone except a science team to go to Genesis, forcing Kirk to disobey direct orders from Starfleet Command and even steal the Enterprise to accomplish his mission. The second threat is from the Klingons, who aren't about to let the Federation develop a weapon that can make, remake or destroy entire planets, which could potentially threaten the Empire.
It's a great storyline which builds intelligently on things established in both the previous film and the original TV series (the finale, on Vulcan, even references the classic episode Amok Time in its set design and appearance). It has the weakness of being predictable - even in 1984 the idea of bringing a dead character back to life for popularity reasons was cliche - which bugged Harve Bennet (a writer of integrity, of the old school) so much that he decided that Kirk had to pay three unexpected prices for the restoration of Spock: the loss of his ship, his career and his son. It's surprisingly brutal: the off-hand murder of David might only be bested by the death of Tasha Yar in Star Trek: The Next Generation for sheer callousness. But it also fulfils a basic tenet of storytelling: your characters can't win something big without a correspondingly massive loss, and one of the reasons why The Wrath of Khan is a classic and The Search for Spock a very good film, and why the much later Into Darkness is such an emotionally hollow and narratively inept remake of the same storyline.
The Search for Spock is also a hugely iconographic film. It introduces a whole range of ships, designs and concepts that dramatically expanded the scope of the Star Trek universe. The Earth Spacedock is a still jaw-dropping design, a massive orbital station that utterly dwarfs the Enterprise. The USS Excelsior, the B-52 to the Enterprise's B-24 bomber, is one of the very finest starship designs ever made for the franchise, so much so that the later Enterprise-B would be of that class and the design would become the Federation default standard by The Next Generation and Deep Space Nine. There's also the fabulous Klingon Bird-of-Prey warship, easily the most famous non-Federation design in the franchise. Even the design of the accessibility-challenged USS Grissom would go on to become a mainstay of future TV shows.
The vfx are more numerous and more sophisticated than The Wrath of Khan's and two sequences stand tall as among the very best in the franchise: the Enterprise spacejacking, probably the most tense "reversing the car out of the garage" scene in cinematic history (with James Horner's God-tier soundtrack lifting the sequence onto another level), and the later destruction of the same ship, which brought a lump to the throat of every Star Trek fan on the planet at the time, before they decided to do it every fourth film for "shock value."
There are, however, several weaknesses the movie has to overcome. Aside from the predictability of the plot, despite attempts to off-set it with greater losses elsewhere, there's the under-servicing of the villain. Christopher Lloyd gives a superb performance as the Klingon Captain Kruge, but he's not well-served by the script. He has several great moments, such as where he orders the death of his lover when he realises she's seen sensitive information and his stoic embrace of death in his final battle with Kirk, but he spends the rest of the time barking out rote threats. You get the impression that if he'd been given the kind of material given to Montalbán in the previous movie and later (in Star Trek VI) Christopher Plummer, he'd have delivered as equally killer a performance, but the lack of good material holds him back. Another weakness is Shatner returning to a more lacklustre performance. He's good in a few scenes (his unblinking and unwavering commitment to stealing the Enterprise, his joy at Spock recognising him in the film's closing moments), but otherwise Nimoy fails to get the same kind of nuanced and vulnerable performance as Meyer did in the prior movie.
The script overall feels a little lacking. There's some good lines and humour, particularly for McCoy (DeForest Kelley relishing a greater turn in the spotlight in Nimoy's absence), but the script lacks the epic scope of The Wrath of Khan. Although Bennett wrote both movies, Nicholas Meyer gave a huge spit and polish to the second film's script which added all of its character and thematic depth. Without his influence, Bennett's more bare-bones script (punched up a bit by Nimoy to add more humour) has less going on. It's not for want of trying though, and it's nice to see the supporting actors finally given more to do: George Takei's Sulu gets a solo action sequence, Nichelle Nichols's Uhura gets arguably her best scene in the franchise despite being absent from most of the film and James Doohan's Scotty gets a gleeful scene after sabotaging an opposing vessel.
Similarly, the film's themes feel a little undersold. Kirk takes preposterous risks to get Spock back, paying a heavy price in the process. Both Sarek and Spock are aghast at what Kirk has done to save Spock, but the film never really adequately gives Kirk time to process his losses and to ask the tough question of if it was worth it. Kirk tries to answer this in the movie's finale but it feels like it could have been explored in greater detail.
The film also suffers from budget issues. This is a more ambitious film than Wrath of Khan on not a much greater budget, and very obvious corners are cut. The Excelsior bridge feels more like it came off a contemporary episode of Doctor Who than a multi-million dollar movie. All of the outdoor scenes on the Genesis Planet are filmed on a set, which is effective in some scenes and all-too-obvious in others. The finale, where Kirk and Kruge's not-very-obviously-disguised stunt doubles awkwardly punch one another whilst the polystyrene set crumbles around them, recalls some of the less-accomplished moments of the original Star Trek series. Again, James Horner's score comes to rescue even in these weaker moments of the film.
Star Trek III: The Search for Spock (****) holds the distinction of being probably the most underrated film in the franchise. A whole raft of iconic moments, some fantastic ship designs, an outstanding musical score and a script that understands that if you're going to pull off something huge, you need to pay a massive price (something that only Avengers: Endgame seems to have understood out of contemporary epic SF movies) are undercut by budget issues, an under-utilised villain and a less-sophisticated script that its forebear, but this is still a fine slice of enjoyable Star Trek action.