Revealing mistake: During the final confrontation in Veidt's lair, you see the actor Billy Crudup in his SFX suit reflected in Nite Owl's goggles, not the image of Dr. Manhattan.
Revealing mistake: In the scene in the Vietnamese bar, after the Comedian shoots his ex-lover and she falls to the floor, the camera shows a quick, panned-out shot of Dr. Manhattan and the woman on the floor. The bottom of her shirt is flipped up, revealing straps of the false pregnancy stomach she was wearing.
Revealing mistake: When Dr. Manhattan is interviewed on TV, his ex-girlfriend Janey makes a surprise appearance in the television studio and launches into emotional accusations. In one shot, we see both Janey shouting in the background and a live television monitor close-up of her face in the foreground. However, the TV monitor close-up shows Janey making completely different head movements than she is making in the background.
Revealing mistake: In the scene in which Dr. Manhattan is dressing himself, as he turns his head at the end, his CGI neck can be seen going through the collar of his shirt.
Revealing mistake: When Dr. Mahattan and Silk Spectre are on Mars and they are climbing upward in his gyrating clockwork structure, a shot from well above, behind and to the right of them contains some terrible CGI work of Silk Spectre walking in a completely unnatural, very mechanical way.
Revealing mistake: When Veidt and his cat Bubastis is walking over the bodies of the scientists after he poisons them, you only see Veidt's reflection and not Bubastis' in the energy panels on the walls as he walks towards and up the stairs.
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