Doctor Manhattan describes a "circulatory system" appearing on the grounds of a government base. However what is depicted is clearly the nervous system, as it features a brain and spinal cord, but no heart or lungs. (This error is repeated from the novel.)
When Adrian/Ozymandias is being interviewed in his office the reporter states that he is the second Watchmen to reveal his secret identity the first being Hollis Mason/Nite Owl I. Mason was a member of The Minute Men (the precursor to The Watchmen) which didn't form until he had retired and passed the Nite Owl mantle to Dan.
When Nite Owl and Silk Spectre II first arrive at the prison riot, the first one to run at them is an inmate with long hair. Silk Spectre II kicks him to the ground. As they fight their way down towards the guard, the same man is seen again and he is then swept off his feet and clotheslined to the ground by Nite Owl.
In Dan Dreiberg's underground laboratory, Rorschach rather pointedly drags his finger through a thick coat of dust over a cover on his work bench to indicate its lack of use. Later when Laurie Juspeczyk pulls the dust cover off of the "Archimedes" ship, there is no cloud of dust.
In the main titles, Nite Owl stands up and his head completely covers the "1940" on the sign behind him. In all subsequent shots of the photograph of "Minutemen 1940" the banner hangs unobstructed above his head.
When Rorshach kicks in the door at the child murder's house, the door bounces several times against the wall, showing a spring is holding it open so it won't swing back in the actor's face. When the murderer gets home a few minutes later, it's standing only an inch or so open.
When Rorschach searches the Comedian's apartment following the crime scene investigation, after jumping from the window he searches the place with his flashlight. He shines his torch to his left (towards to kitchen), but the next shot shows the light shining over the picture of Sally Jupiter with the knife stuck in it (the opposite side of where he points his flashlight).
(at around 5 mins) During the opening fight, as the Comedian is thrown across the room, Director Zack Snyder can be seen huddling between the drawer and brick wall, lower, left-hand corner of the screen. (Snyder points this out during his "live" Blu-Ray commentary.)
In the scenes on Mars, two moons of approximately the same size as ours can be seen in the sky. However, the larger moon, Phobos, is 1/4 the apparent size of our moon when viewed from Mars, the other moon, Deimos, is much smaller - 5% of our moon's apparent size. Neither moon is as spherical as depicted, nor clearly visible from the surface.
When Dr. Jon Osterman's physical body is destroyed in the intrinsic field separator there is a point where the muscle and organs have been largely disintegrated off his remaining skeleton. At this point Dr. Osterman lifts his arms shortly before the rest of his skeleton is completely disintegrated. This movement of his skeleton wouldn't be possible because the muscles necessary for skeletal movement are already gone.
Some of the floating credits are reflected in Neil Armstrong's helmet. The back of the letters (or the reverse side) is what is facing the helmet. The reflection of the reverse side (or, the reverse of the reverse side) would show the text properly oriented. Therefore, both the credits and the reflection should appear as readable; the reflection should not appear backwards.
When the Comedian's coffin is being lowered into the grave Dr. Manhattan's glow is not reflected off of it. This is because Dr. Manhattan can control his skin pigment, as well as the glow he emits. One would not be glowing at a funeral, so Dr. Manhattan in turn is not.
If you look closely at all the framed newspaper articles, especially in the opening credits, the articles themselves are just series of repeating texts and paragraphs. However, this may be intentional, as it is a convention in comic books/graphic novels for "minor text" to appear as scribbles or repeating text.
In this movie, the United States won the Vietnam War. However, one of Veidt's monitors is playing Rambo: First Blood Part II (1985), a movie about avenging America's losses in Vietnam. In Veidt's world, Rambo must be regarded as an imaginative science fiction movie set in an alternate universe.
Dreiberg microwaves a carton of Chinese food with its metal handle still attached. While microwave instructions commonly prohibit customers from placing metal inside them for safety reasons the dangers of doing so are greatly exaggerated in the public mind. Small amounts of metal, like the handle from a Chinese food container, will likely not cause sparking and will generally, at most, cause damage to the microwave not a larger fire or an explosion.
When the reporters are talking to Veidt in his office, they refer to him as being only the second hero to reveal his identity, after Hollis Mason. It is true that in the opening montage, a bomber is seen with Silk Spectre's alias "Sally Jupiter" emblazoned on its side. Her real last name was Juspeczyk. She assumed the name Sally Jupiter because she did not wish to be known as being Polish. No one would be able to just look her up in the phone book so she did not really reveal her true identity.
If you watch the shadows on Dr. Manhattan carefully, it appears that the blue light is coming from an off-camera source, not his body. When he turns his head, the side of his face that is in shadow will change. When he is sitting on the bed holding the bra, the shadow of the bra on his chest indicates this as well. (Note: while the actor was emitting blue light from his motion capture suit during production, the computer model of Doctor Manhattan must be lit independently by animators.)
In Antarctica, as Rorschach and Nite Owl II slide open the doors when entering the facility, there are conduits and pipes on the right side of the screen that should continue through the wall but do not go anywhere. The sliding door passes through the wall where the pipes/conduits should be going. Also, the large pipe has a match outside but the perspective is not correct to have it meed up with the pipe from inside.
As the camera zooms out from the crime scene at The Comedian's apartment, the Chrysler Center is visible in the reflection of the glass, but is not visible as the camera zooms out far enough to be able to see where it should be.
After the fight between Veidt, Rorschach and Nite Owl II, Rorschach helps up Nite Owl as Veidt starts heading up the stairs. Rorschach had his hands at his sides, then the angle changed to over Veidt's shoulder and Rorschach's hands were inside his coat's pockets.
The particle accelerator is used to kill other characters, but why wouldn't they come back like Dr. Manhattan did? The other scientists had been killed by poison before being disintegrated. Dr. Manhattan was alive and conscious when he was disintegrated. His backstory also makes it explicit that he was taught how to recreate complex structures starting in his youth.
The American cities destroyed at the end are New York and Los Angeles, notably NOT Washington D.C., the seat of government. However, Moscow and Paris ARE destroyed. New York was shown to have not been destroyed entirely, thus it is reasonable to believe that the other cities were not destroyed entirely either, and the Soviet premier did survive to make peace.
Veidt uses energy from Dr. Manhattan to destroy major cities across the world in order to end war. If he was able to do this, he might have been able to complete his original stated goal of creating renewable energy to end war. However, there is a big difference between using a physical process as a weapon, or as a useful energy source. In a real-life example, nuclear fusion was made into a weapon (a hydrogen bomb) in 1952, but despite all efforts, even 60 years later, the best fusion reactors are still too inefficient to be a practical energy source. So Veidt's original plan wasn't an option in the time frame he was given.
During the final battle in Adrian's Antarctic base, Laurie shoots Adrian with a pistol. It is hard to catch, but she takes this from a guard at Sing Sing during the breakout of Rorschach. Later it can be seen tucked away in her belt.
In the scene where Rorschach is trapped in Edgar Jacobi's apartment, surrounded by SWAT teams, Jacobi's corpse blinks. However, recently deceased corpses will oftentimes show muscle reactions: twitches, gasps and flexures are not uncommon.