This scene is great for many reasons. They originally filmed the scene with the cameras away from the actors, and shot it like candid camera. Apparently, they hired an actual police officer (in the scene) to double as a bodyguard for the actors.

And this quoted information below comes from:
http://mario.lapam.mo.it/films/st4.htm

William Shatner: "Look closely at the scenes in which Chekov grills random passers-by as to how he might find the nearest 'nuclear wessels,' and you'll notice that he's most often soliciting that advice from real-life, unrehearsed, slightly shocked pedestrians. Their resultant looks of incredulity are quote genuine, as most of them just assumed that Walter was simply out of his mind."

Leonard Nimoy: "Up walked this woman with long, dark hair, whom none of us had ever seen before. She paused to listen to Walter, then said helpfully, 'I think they're across the Bay, in Alameda.' Her reaction was so ingenuous and perfect that we included her in the shot, and wound up negotiating a contract with her, so that we could pay her for talking. It was a wonderful accident, from our perspective as well as hers."

Of all the Treks, this one's my favorite. Yes, Khan is still the best story-wise and perfect in it's implementation of the original series, but I liked this one solely for the exploration into the comedic side of Star Trek. Ranks up there with some of the best sci-fi comedies like Galaxy Quest and The Ice Pirates.