Continuity mistake: When Dan returns home after talking to Mason, he finds Rorschach in his kitchen eating beans from a can. After he has finished eating, he throws the second can on the table where it lands next to another can. When he gets up, the two cans have moved significantly apart. (00:20:15)
Continuity mistake: In the flashback to the Watchmen's initial meeting, the Comedian lifts his cigar to his mouth, but in the next shot, both arms are down by his sides. (00:43:10)
Continuity mistake: When Rorschach throws the basket of grease on the convict in prison, the convict covers his face with his hands in pain. In the following shot, his hands are father from his face than they were before. (01:31:45)
Continuity mistake: In "The Ultimate Cut" version of the film (and perhaps the original), Laurie and Dan have a discussion in a restaurant about the attack on Ozymandias. Outside, across the street we see people milling about. As the camera cuts between shots of both characters at the table, then close ups of Spectre, then of Night Owl, and back again, the positions of these people vary randomly, including a seated girl that appears instantly out of nowhere, then a man in a brown jacket walks over to join her, but instantly is seated next to her, then he's seen approaching and sitting down with her. (Timecode is for The Ultimate Cut). (01:41:10)
Continuity mistake: When Kovacs is being interviewed before being given the Rorshach test, a pill bottle is shown on the table in front of him. The front label of the bottle faces Kovacs when first seen, but a moment later, with nobody touching it, the bottle has turned 90-degrees so that the label faces left of Kovacs, toward the camera. (Timecode is for The Ultimate Cut). (01:50:50)
Continuity mistake: When Veidt is explaining how he offed the Comedian and killed the fake assassin, Rorschach launches an attack behind him which Veidt blocks, the shot changes in an instant cut and Veidt is now facing Rorschach. (03:00:35)
Continuity mistake: During the prison fight scene, Silk Spectre's stiletto boot heels are alternatively flat-soled from shot to shot, for the stunt woman's benefit.
Continuity mistake: In the scene where Silk Spectre II visits Nite Owl II at his home, the small mole on her cheek disappears only to reappear again when they leave to visit Hollis Mason (Nite Owl I). It doesn't appear to be a staple of Spectre's makeup in any way and is instead permanent, as it was present when she left Dr. Manhattan to visit Nite Owl (directly before) and on the way to visit Hollis (directly after) as well as through the rest of the film.
Answer: The short answer is that they weren't really trying to. Ozymandias later revealed, and monopolised on, his costumed identity, Comedian was officially endorsed by the U.S.A. Government at the time so his real identity would have been public record, the first Silk Spectre publicly revealed her identity after retiring, though there is no evidence that the current Silk Spectre has. There is no evidence (even in the graphic novel) that anyone tried to hide their identity to the extent that other comic-book heroes like Batman/Superman do. The only exception being Rorschach where even his follow costumes don't know his real identity until they bust him out of prison.
Sanguis