Arguably the best Star Trek: The Motion Picture. Star Trek II is widely hailed as the movie that restored the witty characterization and exhilarating adventure that epitomized the classic Star Trek TV series.
Star Trek II is also a sequel to classic TOS episode "Space Seed", which introduced Montalban's unforgettable villain, Starship Enterprise. Upon awakening, Khan quickly saw the chance to conquer a new era and he immediately attempted to seize control of the Enterprise. Kirk eventually bested Khan and took back his ship; the Captain's solution to his Khan problem was to deposit the would-be conquerer and his people, which also included Khan's future wife, Starfleet historian Marla McGivers (Madlyn Rhue), to the planet Ceti Alpha V, which Khan could then mold to his liking. Tragically, as Khan revealed in Star Trek II, months after they arrived, the adjacent world, Ceti Alpha VI, exploded, which shifted the orbit of Khan's planet and rendered it an inhospitable wasteland. Many of Khan's followers perished, including his wife, and Khan blamed Kirk for decades. Since Kirk never returned to check on Khan's progress, he unwittingly ignited Khan's enmity.
In Star Trek II, the U.S.S. Reliant's Captain Clark Terrell (Paul Winfield) and his First Officer Pavel Chekov were investigating Ceti Alpha VI as a possible test world for the terraforming Genesis Device. However, they were unaware that they beamed into Ceti Alpha V and walked right into a trap laid by Khan. After the Starfleet Officers were captured, Khan itted he didn't know Terrell, but to Chekov, the warlord boasted, "But you... I never forget a face." Khan even identified Chekov by name. However, it's impossible that Khan could know Chekov because Walter Koenig's character didn't the cast of Star Trek until season 2, while "Space Seed" took place in season 1 of TOS. Simply put, Chekov was never there for Khan to meet decades prior.
Amusingly, there is a simple explanation for the plot hole: No one making Star Trek II realized the error - except for Walter Koenig himself. In The Fifty-Year Mission: The Complete Uncensored, Unauthorized Oral History of Star Trek, by Edward Gross and Mark A. Altman, Koenig confessed that Star Trek II's producer Harve Bennett asked him to do a "Trekkie run" of the screenplay for accuracy to series canon. Koenig immediately realized the glaring mistake in Khan's infamous monologue to Chekov and Terrell. As Koenig explained:
There was some dialogue about Khan saying, "Mr. Chekov, I the face" - which he couldn't possibly have since I wasn't on the series when he did ["Space Seed"]. I was faced with the ethical dilemma of mentioning it to Bennett or letting it go. I chose survival as opposed to ethics and didn't mention it. And, in fact, Ricardo didn't even know it. He didn't know that [Khan] hadn't met [Chekov] before.
Chekov is usually a background character, but he played a major role in Star Trek movies with the exception of Star Trek IV: The Voyage Home. Understandably, Koenig feared that mentioning the plot hole to the producers would necessitate rewrites and could reduce Chekov's role in the movie, possibly even switch him out in that scene for another character who was in "Space Seed". So, in order to protect his part, Koenig kept his mouth shut, perpetuating Khan's inexplicable belief that he knows the Russian when they had never met before. But, it helps to realize that Khan is a man in Star Trek II, so his certifiable insanity is the easiest way to explain the Star Trek movies' biggest plot hole.