MONARCH is a straight Shout-Out to Godzilla's title, King of the Monsters.
The page hyping up the second trailer is called "Awaken the Truth." The name of the graphic novel prequel is Godzilla: Awakening. Perhaps a little thematic connection there?
Why do the Male Muto have wings and the Female Muto is much larger and stronger? The winged Mutos need to hop from mate to mate while the Females need to guard their nest. They need to be big and bad by necessity to protect their young from their predators. They are also based on insects, where it is common for females to be larger. If we assume monogamy, flight allows the male to travel and bring food for the female (which he is seen doing, presenting a nuke as a gift to the expectant mother), while the female would stay at the nest as stated.
The skeleton at the beginning of the film is implied to be another of Godzilla's species. Perhaps Godzilla is hell bent on killing the Mutos because he is mourning the death of his mate, just like Joseph Brody.
Considering Godzilla's sheer size and decades of being underwater, it's not really a surprise that he gets exhausted fighting on land. You also have to wonder how long it takes a creature that size to fully switch from using gills to using lungs. Not to mention the buoyancy water provides. Ever notice how heavy you feel when you climb out of a swimming pool after floating around for a while?
The majority of the military seems to be Navy. If one wants to mobilize against an amphibious Kaiju, it makes sense to keep track of him in the water before he can make landfall. Too bad about him being able to swim under a blockade, though.
Godzilla, like the MUT Os, feeds on radiation. He may have soaked up the radiation from the bomb, further saving the rest of the world, and explaining his waking up at the end when he seemed dead. That or he still has cellular regeneration.
Taking the above a little further; one wonders why Godzilla didn't use his atomic breath more than he did...perhaps because doing so caused him to expel so much radiation from inside him that it depleted his energy, making it a weapon of last resort, hence his collapse at the end of the fight. Absorbing the radiation from the nuke was enough to restore and revive him.
Why is Ford prone to Dull Surprise? He's a returning war veteran, having worked in defusing bombs. Think The Hurt Locker. A fellow officer even warns him that coming home is hard to handle. This is a guy that lost his mom as a kid, went to war and dealt with traumatic situations, and as soon as the monsters start appearing, keeps being thrown through life-threatening experiences over and over. He's racking up a lot of psychological damage. There's also the fact that military personnel, particularly one in bomb disposal, would be trained to keep his cool under pressure and not have a major reaction to situations like this. Also note that the Dull Surprise and his non-emotive moments occur when he's in the middle of tense combat situations, where a soldier is supposed to keep a cool head. When he's in a more casual situation, he emotes quite a lot. He nearly cried when confronting his father in Japan and was visibly distraught when he dies.
Dr. Ichiro Serizawa trying to convince the Navy not to use nuclear weapons on Godzilla and the Mutos seems like a forced anvilicious "anti-atomic weapons" Aesop at first. But, take into consideration that he mentions that his father fought in WWII and was there during the bombing of Hiroshima (IE: The broken pocket watch). Who was formerly a soldier during WWII in the original 1954 film? Daisuke Serizawa. And, take into consideration that Daisuke Serizawa was reluctant on using the Oxygen Destroyer against Godzilla in the original film much like how Ichiro Serizawa is reluctant to use nuclear weapons against Godzilla in this one. Not only are there are similarities between the two characters, but it's subtly hinted at that Ichiro is Daisuke's son in this continuity. On another note, both creatures feed off radiation, and if the blast doesn't kill them, it would seriously piss them off. Godzilla, at the very least, was shown to be able to survive a 15-megaton nuclear blast, so even if they do kill the M.U.T.Os, they would have a rampaging Godzilla to contend with.
The traveling Mutos are difficult to track because of the EMPs they emit, but when those happen the military should at least be able to guess that the Muto is right in the center of the field. So how come they didn't realize the Muto was approaching the train carrying their nuke? Because at the time the train was in a forest where there are little electronics. As such, any pulses would go unnoticed because there's nothing for them to affect, making the wilderness a black zone for the Muto.
Why did Godzilla retreat to the sea at the end of the film? He was probably heading to the site of the explosion to feed off of the residual radiation from the bomb blast. Also, the corpse of the female was in the water, not on land.
During earlier attacks, the Mutos don't seem to actively use their EMP as a weapon, seeming to be trying to generate the shockwave the stomp accompanying it comes with. This makes sense, considering it's described more as a natural byproduct of how they feed, so using it offensively makes little sense. However, in the San Francisco fight, the male Muto begins his attack with one. Why? The Mutos are shown to be very intelligent. The EMP isn't a natural weapon. The Mutos LEARNED to use it as one seeing how easily it disabled military weapons.
Godzilla and the Mutos being so tough makes sense when you realize they both came from an era when giants such as them were apparently common place. Just like many creatures with natural armor (such as crocodiles) are resistant to small arms fire, the Kaiju are a massively scaled up version of that. Also, if you think about the square-cube law, these creatures need to be that tough just to be able to support their own weight.
The Mutos being far more aggressive to mankind than Godzilla makes sense. To both creatures, humanity are hardly a threat, so Godzilla seems to just ignore them most of the time, but the Mutos are a mated pair preparing to nest. Animals are naturally far more aggressive when nesting. Also, the Mutos' infants are shown to be human sized at best and likely far more vulnerable than the adults. Also, the Mutos don't seem to attack humans to destroy them at first. The male was mostly trying to escape and find sustenance.
The female Muto seems to be a good deal more aggressive towards humanity than her mate, best shown during her rampage through Las Vegas when she actively tears some buildings down that weren't in her path. Remember that, while the male was mainly observed inside his cocoon, the female was said to have been tested heavily and even partially cut open before it was believed she was completely dormant or dead. It's quite possible she was vengeful.
Architectural studies have shown that a pyramid is the most stable structure possible for a building. So it's not because of pure luck that the Transamerica Pyramid is left standing at the end.
A meta-example: The Mutos bear an uncanny resemblance to the Cloverfield Monster, who's own movie was stated to be the "American Godzilla". Godzilla thoroughly thrashed both Mutos can be seen as the former taking on the challenge to his title, and winning. King of Monsters indeed.
The nukes the Mutos are seen gobbling up throughout the movie have been referred to as snacks many times, including on this very site, but they would likely be better described as a 3-course meal in a stick of chewing gum. The fuel used in nuclear weapons is required to be very pure, and when enough of it is put together it spontaneously begins emitting critical amounts of radiation and detonates. If the monsters feed on radiation, then a single nuke should be more than enough to satisfy them for a while. The Mutos had found the perfect meal wrapped up and ready to go, and they weren't about to pass up the opportunity to eat as much as they could.
Godzilla has never really looked like a dinosaur, and although the 90's films established him as such, it applies only to that incarnation. For this film, he's explicitly defined as something else; he predates dinosaurs by hundreds of millions of years. Before the Mesozoic era, the Earth was populated by Synapsids, which are considered a proto-mammal of sorts and are roughly described as "mammal-like reptiles." Despite having more than a few resemblances to dinosaurs, Godzilla has more in common with Synapsids and thus resembles a sort of proto-mammal himself, which explains the unique shape of the head.
It's also possible that Godzilla's species could be a type of Archosaur. Archosaurs are a group of reptiles that first appeared in the Permian era (when Godzilla's species first appeared) and whose descendants include dinosaurs, birds, and crocodilians. Given Godzilla's aquatic nature, armored scaly hide, and predatory nature, it's possible his species could be a form of ancient ocean-dwelling Archosaur. Perhaps even some sort of prehistoric crocodile, especially when you consider that the earliest species of crocodilian (such as Protosuchus and Simosuchus) looked more like Godzilla than modern-day crocodiles.
The plan to use the force of the nuclear explosion to kill all three kaiju actually makes sense (despite their ability to feed on radiation) in the context of Awakening. That's exactly what killed Shinomura, which could also feed on radiation. It didn't work on Godzilla the first time, but assuming it would kill the Mutos is reasonable.
When Godzilla first arrives in Hawaii, he causes a massive tsunami. But every time he exited the water afterward, there was very little water displacement. For all this talk about how smart the MUTOs are, Godzilla is just as smart, if not smarter, and probably realized the damage he caused, and as such, every time he's shown exiting the water after his initial appearance, he's shown moving much slower, preventing him from inadvertently killing more innocents. (Remember, when he got to Hawaii, he had more or less raced across the entire Pacific.)
The reason Elle lost the phone connection while trying to get in contact with Brody after the Male MUTO escapes Janjira? EMP! The general said that the MUTO messed with the satellites they would have used to track it, and guess what many phone calls go through!
Why does Godzilla seem strangely benevolent towards humans? Godzilla and the other kaiju in this setting feed by absorbing radiation, and Godzilla not only was lured to the surface (accidentally) by an American nuclear submarine, he was subjected to repeated atomic bombings during the 1950s. Humans also tend to spill more ambient radiation than nature alone provides. He's probably learned to associate humans with food, and is smart enough to try and repay them for their "kindness" in their unintentional efforts at handfeeding him. This would also be an excellent Mythology Gag; during one part of Toho's Godzilla, "Junior" was benevolent towards humans in part because they had set up specialised nuclear reactors where he could come, peacefully draw off a charge of atomic energy to feed himself, and then leave without being hassled.
Godzilla's fighting style is based primarily on that of a bear. For those of us who are uncomfortable with youtubing what Bears do when fighting, they roar, then slam their massive bodies against their opponent. Thrashing their claws into their side until they are taken to the ground. All the while digging their teeth into them. The Horror part? This type of fighting style will be implemented with a beast 350 feet tall...
Creatures from the old world fed on radiation, making them great big batteries —hence why the Muto chrysalides were found stuck to the skeleton of another of Godzilla's species. So, had Godzilla lost the battle... Femuto would have likely ripped him open and laid more eggs inside him. Probably why Godzilla wanted to kill the Mutos in the first place. Kinda like how hyenas and lions want to kill each other. They are each others natural enemy, and since the two Mutos are actually capable of matching Godzilla (and presumably hurting him) in combat and both feed on radation, probably rival predators as well.
How many people died over the course of the movie, in Honolulu, San Francisco, and Las Vegas?
Remember the submarine? The 10,000 ton one picked up by Hokmuto like a eagle picks up a fish? Imagine how strong the male Muto has to pick it up and fly as fast as it did?
Speaking about the submarine...do you think there were any survivors?
Just how intelligent the Mutos are. These are creatures massive beyond imagination, who are capable of learning. Imagine if these creatures ever became smart enough to see humanity as an active threat...like they do when their eggs are destroyed.
Godzilla was shown seemingly trying to avoid wanton destruction, yet kills hundreds of people anyway. Imagine what's going to happen if he does go on a rampage like he usually does...
The MUTO pair and Shinomura were both super ancient monsters laying dormant deep below the earth until awakened, and Godzilla has been around for just as long. While this gives the writers an easy way to introduce new monsters in the sequels, it still raises the question of just how many titanic, sapient disasters lay dormant below the Earth's crust, just waiting to awaken and be unleashed.
Remember how strong the female MUTO was during the fight with Godzilla? Ponder this for a moment: She'd just laid her eggs not too long before Godzilla arrived. Most animals are severely weakened and tired after giving birth...
The fact that Godzilla was part of an actual species. One of him is already terrifying and destructive enough, imagine if there were more of him. Good thing he's The Last of His Kind right?... Right?
When we finally get to see San Francisco burning, you got to ask yourself, how many people couldn't get to safety in time?