Star Trek creator Gene Roddenberry was ousted from the project and the reins were handed over to producer Harve Bennett. A non-Trekkie, Bennett watched every episode of the TV series and determined that the first film lacked two ingredients: (1) a dynamic villain and (2) an emphasis on the on the “triangle” of Captain Kirk, Mr. Spock, and Dr. McCoy.
The coincidental aspects of the story are a bit hard to swallow, but co-writer/director Nicholas Meyer zips the plot along so speedily that one has little time to notice. I really like how he crosscuts from Kirk to Khan to the Genesis team as they all converge on the same location.
With its back-to-basics approach, Star Trek II: The Wrath of Khan laid the groundwork for the rest of the Trek films and pretty much saved the Star Trek franchise. It also forms a trilogy with the Star Trek III: The Search for Spock and Star Trek IV: The Voyage Home (their plots are connected, whereas the last two films are stand-alone adventures).
In addition to Wrath of Khan, writer-director Nicholas Meyer was also involved in the next two best series entries in the series: The Voyage Home (an amusing time travel adventure) and Star Trek VI: The Undiscovered Country (an effective mix of politics, sci fi, and mystery). Meyer, whose filmography is surprisingly short, also directed another time travel tale: the classic Time After Time.