The concept of "Alpha of the Titans" relies on the theory of "Alphas" in wolf packs, with the Monarch scientists explicitly referencing said theory, despite it being debunked about 20 years before the film's release (by the same scientist that originally proposed it, no less!). That said, the idea could still work in terms of the Titans, since the old idea of "Alphas" can form amongst unrelated individuals forced into a pack, which is basically what is happening here (although a scientist referencing this idea straight still falls under artistic license).
The oil derrick-covered dusty plains that Scylla emerges from, is stated to located at Sedona, Arizona, despite, actually resembling West Texas than the oil-free red rock mountains actually found there.
On the touch screen guide to the locations of the Titans, the Titan in Australia is listed as being located at Ayers Rock. The name was officially changed to Uluru in 2002. The name comes from the Pitjantjatjara Anangu, the Aboriginal people of the area who are the traditional landowners of Uluru.
The fictional Isla de Mara, geographically placed at the border between Texas and Tamaulipas, is too far North to exhibit the kind of tightly-packed, colonial Spanish architecture shown in the film. This type of urban layout and construction is more appropriate to colonial towns in Central and Southern Mexico. (To wit, street-level scenes were in fact shot in the preserved historical district of Santo Domingo in Mexico City.
When there is a pan out of Fenway Park you can see The Charles River, on the river is a navy destroyer, there is no way to get a ship that large all the way down the river to that area, all bridges are to low and the locks at the Museum of Science are to small.
Godzilla makes landfall from the Charles River. But one in-between shot shows him stepping out of the Boston Bay at the Financial District, several miles East, with the Monarch fleet in tow. (There's also the issue of Godzilla having to take a circuitous route to navigate the Charles, which is too shallow to accommodate a creature of his girth, instead of just stomping into town directly from the ocean.)
The location of Skull Island shown on MONARCH's big map (somewhere far south and somewhat east of Hawaii) makes absolutely no sense considering a dogfight happened there between an American and a Japanese pilot in 1944.
Social animals rarely, form packs with members of other species (in the case of wolves, packs are pretty much exclusively members of the same family), so the idea that all the wildly different Kaiju are forming a pack is a pretty big stretch. It's implied Ghidorah has some unique ability to make the Kaiju obey him, but the human characters are still using faulty logic when they scientifically use the "pack" analogy.
The monsters are stopped by transmitting the Alpha Call over the loudspeakers at Fenway Park in Boston. Allowing for the speed of sound, it should have been hours before many of them heard it, but they all stopped at once.
The idea that radiation can generate new growth in barren landscapes or lead to a resurgence in the populations of endangered species. While it is true that radiation can spur the evolutionary process by increasing DNA mutation rates, this is only feasible at fairly low rates of continuous exposure (such as a small percentage increase in UV rays due to ozone depletion). The kind of radiation that Godzilla and the other Titans pump out would only serve to give most ecosystems harmful acute radiation exposure, given that biological processes that run on radiation is dubious at best, it makes more sense, as the Titans absorbing "bad" radiation, processing it in their systems and excreting it as "helpful" waste radiation.
Godzilla, Mothra, Rodan and the other Titans are classified under the genus "Titanus". In reality, the genus is reserved for a group of very closely related species ( lions, tigers and leopards), so seeing arthropods, reptiles, mammals and cephalopods all lumped together into such a specific group makes no sense, however it could be interpreted as a code-name and not as a strict scientific name.
Social animals rarely, if ever, form packs with members of other species (in the case of wolves, packs are pretty much exclusively members of the same family), so the idea that all the wildly different Kaiju are forming a pack is a pretty big stretch. It's implied Ghidorah has some unique ability to make the Kaiju obey him, but the human characters are still using faulty logic when they unironically use the "pack" analogy.
This movie states that Ghidorah is a fairly recent discovery thus Monarch has had little time to study him. Except that the post-credit scene in Kong: Skull Island, set in 1973, shows that Monarch knows about him along with Godzilla, Rodan, and Mothra.
When Madison Russell is trying to run out of the booth in Fenway Park, Ghidorah is busy blasting the place to smithereens. A large concrete block is dislodged on the stairs Madison is running down and actually bounces off of her. In reality, that block would have caused major bodily harm or even death given it's large size (about ten feet square).
The 50-second teaser trailer video shows Madison, listening to a radio at what looks like an underground bunker. She recoils in fear as she begins to hear Godzilla's iconic growl. At around the 30-second mark in the clip, the camera pulls out into a wide shot, which reveals another camera behind her. The rogue camera comes closer and for a moment, occupies a large chunk of the shot.
Not only is the camera easy to spot, it's a major error on the part of the Godzilla marketing team.