During the first attack when everyone runs outside of the apartment building, Lily can briefly be seen wearing white sneakers even though she has high heels on during the rest of the film.
The helicopter crashes towards the finale, yet the characters are able to walk away with only minor injuries. If the crash was a straight 400-foot drop, this would obviously be impossible, but the helicopter as attacked and damaged, and did not instantly fall from the sky like a rock. A trained pilot would be able to achieve a semi-controlled landing via auto-rotation even in the event of a complete engine failure.
We see Lily wearing gold heeled shoes throughout most of the movie. Then when the group are walking up the stairs to cross to Beths Apartment she takes her shoes off. A Short time later when Lily, Hud and Rob are crossing to the Apartment roof, Lily is wearing Gold flat footed shoes, not the heels she was wearing before. Her shoes then change back a short time later.
"In the movie, footage is shown being recorded over existing footage, as if the camera were recording on digital or analogue tape. Rob and Hud even discuss whether the tape was changed during the party. However, the title card at the beginning of the film claims the footage was recorded on an SD card." The footage was captured on tape, and after retrieval was later transferred to an SD card by the Department of Defense along with overlaid official document reference codes, a time counter, and the watermark "PROPERTY OF THE U.S. GOVERNMENT, DO NOT DUPLICATE", which can be seen at the very beginning of the film.
It's clear that Rob didn't record for 7 hours. There are about 70 minutes of footage in the movie, so the battery would only have had to last that long. Most consumer digital cameras, even battery-hungry miniDV devices, boast a recording time of more than 2 hours on the supplied battery pack, and on the order of five hours on the manufacturer's high-endurance option.
From the time Hud first spots the monster in the helicopter to the time the helicopter crashes is less then a minute, yet the time changes from night to sunrise. However, the military man that told them of the helicopter told them that the last helicopters would be in the air by 6:00 am. The time from the crash to the time when the camera restarted recording is unknown, but it is possible that the sun began rising at that point. Even their visibility in the helicopter was getting much better and looked like the early dawn.
The time stamp on the camera disappears after Jason gives his testimonial to the camera. Considering Hud had no idea how to use the camera, and the option for time stamping is often a button on the side, it is very easy to conceive that the button was pressed at some point during the video. However, it is most likely a creative decision by the Director, as the time stamp would be annoying to view the entire time of the film.
When Beth and Rob are sitting under the bridge at the end of the movie, Beth has her left arm up, touching her head. This should be impossible or at least excruciatingly painful as her left shoulder was pierced by a steel bar earlier in the film.
After the initial attack with the Statue of Liberty head laying in the street and everyone emerges from the store, Hud starts exclaiming that he has footage of the monster, and everyone gathers around Hud as if he is going to play the video. The footage cuts to some additional footage that Hud is supposedly taping over, and then the image resumes, as if Hud turned the recording feature back on just after everyone has seen the footage, and is reacting to the sight.
The problem is that if Hud rewound the tape back to show the footage of the monster, and then stopped the footage just after the monster appeared on the screen, then started recording again, he would have taped over everything that happened after he saw the monster (all of the footage in the store, for instance). Not enough time had elapsed between him showing the footage and his audience's reactions for him to fast-forward again to a spot after the footage we saw of him exclaiming he had images of the monster.
As the Statue of Liberty's head strikes the high rise, there is a large and fiery explosion. The statue itself is composed of iron and copper, and the head is hollow, yet the impact causes an explosion akin to that of artillery fire. However, it is very likely that this is a residential building, and therefore likely to have gas lines, which could easily rupture and explode after such a catastrophic impact.
Coming through the Narrows from Lower New York Bay (off Coney Island, where the monster was awoken) and onwards to Liberty Island (where the monster first makes its presence felt) there's no straight-line path that would subsequently put the monster in lower Manhattan. If it continued on a straight line from here it would wind up in Jersey City or Union city. However this assumes that the creature would continue in a straight line. Given that the monster is a disoriented, angry sea creature, and that it negotiated the Narrows to stay in the water until it came across Liberty Island, it's not unreasonable that it returned to the Upper New York Bay after attacking the statue instead of pushing onwards over land. If it continued inland up the Bay, it would inevitably run into Manhattan Island as we see in the movie.
When Rob runs over to the electronics store, Hud tells Marlena, "I'll go get her."
In the theatre, it is obvious that the footage is of very high audio-video quality, including multi-channel surround sound and ultra-high-resolution video at 24 frames per second, typical of movie productions, as opposed to 30-frame-per-second digitally compressed video with stereo sound that can be created with most consumer video. However, this is a necessary and deliberate change on the part of the crew, and not an error. Producing a movie with "authentic" quality based on the equipment Hud is carrying would have produced a very poor result when projected onto hundred-foot screens, and incompatibilities in frame rate between a 30-frame-per-second recording and the 24-frames-per-second provided by movie projectors would have created a movie which was unusable to most theaters.
During the subway tunnel scenes, Rob's shirt seems to clean itself. At first it is dirty and sweat stained, then it is relatively clean, and then it is dirty again.
When everyone sees the explosion from the rooftop, the explosion (and bits of debris flying from it) appears very far away. But, by the time Hud has turned around, the flaming debris has already reached the rooftop.
When the main characters are caught between the monster and the Army's attack, we briefly see what appears to be a truck mounted with an MLRS pod launching missiles at the monster. There is no 'rocket truck' like this in the U.S. Army. The closest equivalent, the M142 HIMARS, does not resemble the one in the film. Moreover, each rocket from an MLRS pod would have been much more powerful than is shown, both in the impact and the blast as the rocket is launched.
No camera comes with an integrated light (which it is obviously as Hud must be pointed to it) that has such power as it is seen in the tunnel.
(at about 50 minutes) During the military medical scene a communications officer reports that they have "two F-18's en route from Selfridge". Selfridge ANG in Mount Clemens, MI house F-16's, not F-18's.