The Category scale used for the Kaiju is called "Serizawa".
Speaking of the good doctor: Remember what humanity's last-ditch effort to stop Godzilla ended up being? A small party of humans took a superweapon down to the ocean bottom and detonated it in the monster's face. At least one member of the party stayed below as part of a Heroic Sacrifice. Sound familiar?
A modified version of Godzilla's roar can be heard during one of the opening montage of past Kaiju attacks.
During their introductory sequence, both Godzilla (in the 1998 American film) and the first Kaiju make landfall on bridges in traffic, both under white skies, both of which being giant CG things obscured mostly from view, and both incoming from right of frame from the sea. And then the next Godzilla movie does it again.
A subtle one, the Aliens sending the Kaiju live near a star apparently being sucked into a black hole. One alien race in the Godzilla series (and only one to make multiple appearances) are space apes who are trying to take over the earth for the exact same reason.
After the one of the Kaiju of the Hong Kong battle, Otachi, reveals that holy shit she can fucking fly she starts making sounds very similar to King Ghidorah and Rodan.
All the kaiju have two brains, just like Godzilla.
The scene in Tokyo focusing on a horrified child watching the carnage is likely an homage to a particularly heart-wrenching scene in the original 1954 Godzilla of a mother and her children hiding in a Tokyo alleyway and knowing that they're all about to die.
Newt's remarks about pollution allowing the Kaiju to survive in Earth's biosphere bring Godzilla vs. Hedorah to mind.
When the category 5 kaiju emerges from the rift, the musical motif is very reminiscent of the motif that plays when Godzilla rises from the ocean.
The aliens in both films are Planet Looters who have wiped out the inhabitants of countless other planets in order to harvest their resources, and now have their sights set on Earth. Only here, instead of using city-sized destroyer ships, they attack from beneath the ocean via manufactured monsters. Hell, they even look similar to the Independence Day aliens.
Gipsy Danger seems to be one to classic Super Robot, specially to Mazinger Z given it has not just Rocket Punch but also Breast Fire. In addition to functional nods to classic Super Robot, and despite Del Toro's claims that he avoided visual references to established mecha, Gipsy Danger has clear influences from Gigantor, the 1980 anime version specifically. Del Toro explicitly says Tetsujin 28-Go was an influence in one of the pre-release featurettes.
Also, it has a Pilder, though we never see it operate on its own. Although it does have the classic "Pilder, on!"
The detachable head and blasting hole in its torso have an even closer resemblance to another Go Nagai super robot, Steel Jeeg and its Spin Storm.
Brawler Yukon, who appears in the comic, looks like a more humanoid version of the Beetle T-23 scout robot from Getter Robo Go.
In the same vein there's Horizon Brave, with two large shoulder mounted pods that appears during the prologue showing its construction, toy version and post-destruction. It looks a lot like Getter Poisedon albeit more like the tweaked design from Getter Robo Armeggedon.
Del Toro himself admitted, in a Japanese TV program, that Coyote Tango and Cherno Alpha are inspired, respectively, by the Guncannon and a Zaku from Mobile Suit Gundam, specially the former one.
Specifically, it appears to be based on the RX-77-01 version from Mobile Suit Gundam The Origin, with its 3-clawed hands, larger cannons and blue visor.
Related to the above, Striker Eureka has "GN 000" printed on its left chestplate. This is the model number of the 0 Gundam, which becomes more appropriate once Stacker is in the driver's seat.
The helmets worn by Cherno Alpha's pilots bring to mind any number of sci-fi designs, but particularly seem to invoke Votoms and Gasaraki, or perhaps more pertinently the HRL pilot suits from Gundam 00, the HRL being the superbloc that contains Former Russia.
Cherno Alpha's piston punch also works exactly like a Scopedog's.
The nuclear mission is a reference to Gunbuster, particularly the descent into Buster Machine 3.
Hell, Stacker Pentecost IS Kamina. He tells Raleigh "you have no idea who the Hell I am" and his Rousing Speech at the end includes the words "we have chosen to believe not only in ourselves but each other". He channels Gendo Ikari, but deep down he's as hot-blooded as any blue-haired stunner-shades-wearing mecha pilot.
The film is essentially an adaptation of Shinkon Gattai Godannar!! , which also features a twin-pilot robot controlled by an older man who lost his partner in battle and young Japanese woman who was saved from a giant terraforming beast that rose from the ocean by a giant robot and then dedicated her life to becoming a pilot despite her guardian's disapproval. Said robot is also powered by a giant spinning turbine in the middle of its chest and uses detachable air transport to reach its deployment zone. Finally, the fact that there is an international team of robot pilots, with two of the teams being of the same origin as the ones from Godannar (One from Russia and another from China, Gipsy Danger's pilots are a composite of the Japanese and American teams, and the Australian pilots can be construed as expies of the UK Team).
The initial treatment of the Kaiju as simply natural disasters from a dimensional rift is similar in nature to the Heterodyne entities in the anime Dai-Guard.
The entire premise that Jaegers require two or more pilots who are in harmony with one another and share emotions/memories when linked? Can you say Genesis of Aquarion, anybody?
The Jaegers are piloted in the same manner in Robot Jox, except they require two pilots.
It's a bit of a stretch, but there's one crowd scene where there are two helmeted UN troopers standing to the right of Stacker Pentecost's shoulder while he delivers Important Plot. These are the only two helmeted guys clearly visible in the scene - one white guy and one black guy - and they look suspiciously like the two UN troopers guarding the base in the opening scenes of Muv-Luv Alternative. There are several other distinct parallels, including:
the Kaiju are bioweapons created by a race of silicon-based life forms,
the "blue and glowy scanning-microscope image" aesthetic of the aliens,
the leading couple pilot a twin-seat weapon,
like Sumika, Mako has gone through extreme trauma which causes a berserker outburst at an inopportune moment,
a character gets Eaten Alive from behind in a completely unexpected manner while having a conversation with another character. Up until this point there has been little indication, apart from a throwaway comedy line, that the Kaiju find people tasty,
the good guys are part of a project which is going to be cancelled by the suits in favour of a different, and less salutary, alternative,
the leader of the good guys is a dark-skinned guy (Indian in Alternative, Black Brtish in Rim) who gives a rousing speech while the robots are launching on the final mission.
All the talk about MLA and still no mention of one of the most important plot points? : in MLA, Unit 00 (Sumika) connects to the BETA network every time the fluids in her body are filtered, giving her access to the BETA's plans and hive layouts. It works both ways, though: she also unconsciously sends information to the BETA, which spells grave news for the humanity. Sounds similar to Newt's Kaiju drifting and its consequences, doesn't it?
Gipsy Danger's atomic generator allowing it to work in an EMP Field mirrors Giant Robo's ability to function within the Anti-Shizuma field. That the world's last hope lies with an outdated atomic robot also mirrors Giant Robo.
The film explains that the invaders had once tried surveying Earth... with the dinosaurs. Perhaps an allusion to the Dinosaur Empire?
Mako being rescued by Stacker in the flashback is reminiscent of Setsuna's first scene in Gundam 00. "I must become Jaeger!", anyone?
Aside from the name, Striker Eureka bears some reference to the Nirvash LFO from Eureka Seven.
Before the first drift see the helmets of the suits fill with an orange/yellow fluid, a reference to LCL from Eva.
Cocky, egotistical pilot with a chip on their shoulder and family issues, a dead mother, and constantly trying to show off to their parents. Are we talking about the second Striker Eureka pilot, or Asuka Langley Soryuu?
A mech going berserk, thanks to its pilot's memories, and attacking (or, in Gipsy's case, nearly attacking) the control room. Absolutely nothing can stop it, not even getting unplugged. This is a reference to EVA-00 going berserk when Rei was inside it, albeit without headbutting the control room.
The weaponized coolant is very much straight out of "Magma Diver".
The escape pod scene is pretty much Misato's experience of Second Impact. The first pod is even shot the same.
The image of an aircraft carrier bearing Kaiju remains recalls a similar scene in Asuka's debut episode.
The scene is also quite similar to that shown in the 3rd Rebuild film where the badly damaged Unit 02 and Unit 08, salvaged by the Wunder, are strapped to its landing pad in a similar fashion. Bonus points for being badly wounded.
Leatherback is essentially Hellboy's Sammael with a flatter face and bigger arms. He's even got a tentacle mane.
Mutavore's crescent-blade head, forked tail, and single crest-wing resemble the Bio-raptors from Pitch Black.
There's also a creature from Wayne Barlowe's Expedition called a Keeled Slider that has an uncanny resemblance.
The newborn kaiju looks like one of the aliens in Evolution.
Newton and Gottlieb's names are an obvious reference to another very famous pair of occasionally-feuding scientists.
So obscure it might be a coincidence: Newton has a lot in common with Dorohedoro's Dr. Kasukabe: both are smaller-than-average over-enthusiastic scientists with short hair, glasses, elaborate tattoos and a really hands-on approach to studying beings that can easily kill them, to the point of mind-melding with / marrying the enemy, respectively and their research does a lot of good seeing into the mind of the kaiju / knowing how evil magic-users work but also causes a lot of damage the kaiju can read his mind / unwittingly helping the Big Bad become powerful. There's also this parody of kaiju anatomy for Kasukabe's wife, a magic-user who became a devil and can get of her "skin" for a little while.
Gipsy Danger's golden visor also resembles that of Master Chief. Note that Del Toro was considered to direct the canceled Halo movie.
A combination of Master Chief's visor and (best seen when viewed from an angle) Kamina's glasses.
Newton being found by the kaiju in the underground bunker is similar to a scene in A Bug's Life; incidentally, both Newton and Flick the ant are inventors with good ideas that have bad consequences (see Flick's "tunnel-within-a-tunnel project" and Newton drifting into the kaiju's mind and accidentally tipping off the rest of the kaiju "fleet").
The glimpse of the level-5 kaiju being "assembled" when the two scientists drift into the baby kaiju's brain is reminiscent of Leeloo's resurrection.
When Raleigh activates Gipsy Danger's nuclear reactor to overload and destroy the Anteverse, the switch he uses to do so looks a lot like the power switches shown in Mass Effect 3.
Also, Gipsy Danger's arrival is heralded by a very loud horn, much like the Reapers, though less terrifying. Apparently, Raleigh plays it to intimidate the Kaiju, much like how the Reapers do the exact same thing. It's noted that supposedly all the Jaegers have a foghorn to intimidate the kaiju or warn nearby civilians, such as the boat.
In fact, Gipsy Danger's design can evoke the image of an armoured Human Reaper (or a Human Reaper donning N7 armour—think about it), what with the red reactor core resembling a Reaper "eye". It would roughly be around the same size as well.
Cherno Alpha's reactor resembles Doc Brown's reactor found on his DeLorean.