Big-Lipped Alligator Moment: The Light Show at the Pyramids of Giza, with the mystical narration. Though in fairness, this is a case of Aluminum Christmas Trees. If you're at the Pyramids of Giza at night, that light show will be playing. That said, the whole Sound and Light Show (which is still playing today, with the same narration) is basically an hour-long Big Lipped Alligator Moment.
Jaws, who along with Oddjob, Red Grant and Baron Samedi is one of the most popular villainous henchmen of all time. The guy became so popular that he's so far one of the only two James Bond villains that were allowed to return to a sequel and get a redemption, and when people hear the word 'Bond Villain', he's likely one of the examples that will be brought up first.
Anya Amasova gets a lot of love from the fandom as well, given her beauty, brains and hyper-competence to the point that many consider her to be Moore's best Bond girl, if not one of the best overall. Even the producers liked her so much that they asked Barbara Bach to reprise her role on two separate occasions, although sadly she declined.
A rich tycoon wanting to create a new underwater civilization, protected from nuclear warfare? Rapture has you covered.
Roger Moore was in a 1976 Italian action movie called Street People (aka The Executors and The Sicilian Cross). His character drives a car into the ocean, so he tells his partner to get him an amphibious car next time.
The hotel receptionist at Bond's hotel is played by Valerie Leon, who would later go on to play a fisherwoman in Bahamas in the non-EON-produced Never Say Never Again. In this film, she is flirty with Bond, but in an uncharacteristic move for him, Bond closes his room's door in her face; whereas in NSNA, Bond has no such problem and the two end up in bed together.
Ho Yay / Worthy Opponent: M and General Gogol. After British and Soviet forces decide to work together, Gogol calls M "Miles"note Incidentally, the only time in the movies M's real name is mentioned, M calls Gogol "Alexis", and they act positively chummy with each other. Bond and Anya give a WTF look to each other after witnessing this scene.
Memetic Bystander: The guy drinking wine when the Lotus surfaces at the beach. Not only does he reappear in the following two films, he's slowly developing a meme.
Rooting for the Empire: Richard Kiel has recounted how Jaws' survival at the end was met with giant applause at several screenings. He might be a villain, but he's such a Determinator that after a while you sort of root for him.
Sacred Cow: It is unanimously considered to be the best movie of the Roger Moore era, and is the only movie of the 70s and 80s that has not divided fans' opinion.
Squick: When Stromberg drops his traitorous secretary into the Shark Pool, the shark puts its snout right into the secretary's crotch.
Unintentionally Sympathetic: The intention during Bond's fight with Sandor was presumably that the woman Bond meets was in league with Sandor and drawing him into position to be shot, similar to the scene in Thunderball where Fiona tries to trap Bond the same way. Unfortunately, this isn't quite made clear in the scene itself, which can give the impression that Bond coldly sacrificed an innocent bystander just to save his own skin.
What Do You Mean, It's Not for Kids?: Jaws gets stuck to a giant electromagnet because of his metal teeth, then dropped into a shark tank. Stromberg murders his secretary for betraying him by feeding her to said sharks, and Jaws gruesomely murders two people offscreen and nearly murders two more onscreen.
Win Back the Crowd: It had been years since there was a great and successful Bond film. Then this movie came out, and the franchise was revitalized.