I’m not even trying to analyze these references, just catalog them (please comment and add any I missed). Of course, this means spoilers…
First, Gipsy Danger is basically Mazinger Z. This is most visually apparent when she’s flown into the battle in Hong Kong and her silhouette through the fog is exactly Mazinger’s, but also because GD does a couple of things that are direct and obvious homages to Mazinger behaviors:
- Jet Elbow = Rocket Punch. Not much else to say here
- GD twice expels flame from her nuclear heart, once to slow her fall and once when fighting her final kaiju opponent; this is Mazinger’s Breast Fire
- The way GD’s head is a separate module that falls into and merges with the rest of her body is basically Pilder On (I mean, the Pilder is a vehicle in its own right, but still)
(Incidentally, this relationship to Mazinger is why I’m using a gendered term for a robot – I’m hoping Gipsy Danger gets a guest spot in the new Go-Nagai-robots-as-moe-girls anime Robot Girls Z)
The Kaldanovskys (pilots of the Russian jaeger Cherno Alpha) wear helmets that strongly resemble the heads of Scopedogs from Armored Trooper VOTOMs.
Also, this may seem too obvious but…Raleigh originally pilots Gipsy Danger with his brother Yancy. His big brother. Anime is pretty clear about what happens to cool older brother characters who pilot robots (Macross, Gurren Lagann, I can’t even imagine how many other shows…)
When the kaiju in Hong Kong fires a blast that disables digital electronics but Gipsy Danger is still operable because she’s “analog” (lol) that’s a nod to Giant Robo from OVA series Giant Robo: The Day The Earth Stood Still, and the fact that it’s able to remain operational against the Eye of Von Vogler because it isn’t powered by a Shizuma Drive but a nuclear core. The fact that GD has a nuclear core (relevant to the final battle) is another nod to this.
Not exactly anime, but the voice of the AI in Pacific Rim is the voice of GLaDOS from Portal.
I’m not sure if giving characters names like “Stacker Pentecost” is a nod to Gundam/Tomino-esque naming in general.
And…that’s everything I can place at the moment, but I know there are others. I’ll add more as I think of them, and again feel free to educate me in the comments.
Percent Liar 
I don’t know how much stuff in PR is deliberate reference, and how much is a result of immersion in its 70s influences; GdT says in the robot design documentary that the designers worked with a ‘no direct references’ rule, which might explain why none of the correspondences are /exact/.
But, FWIW, I noticed that Cherno Alpha appears to be able to jolt its fist forwards from its arm like the Scopedog can — it does this with its right hand shortly after the elbow drop, if I remember rightly.
As Dave’s Colony Drop post pointed out, the grizzled commander slowly dying from a disease which conveniently only manifests itself as something like nosebleeds or coughing up blood is an anime topos (and especially a Yamato thing).
The use of Gypsy Danger’s reactor as a bomb echoes Gunbuster but I suspect the real influence there, if there is one, is from Getter Robo (presumably also where Gunbuster took the idea from). On that note, Gypsy’s ‘Breast Fire’ is like a combination of Breast Fire and the Getter Beam — its position in the centre of the robot, a bit lower than the upper chest, and its circular shape are more like the latter.
The way that the kaiju collective consciousness gleans its own information from the scientists brain-diving the kaiju brain and then intelligently uses that information to defend the Breach is pretty much exactly the same as a major plot point in Muv-Luv Alternative; and the agenda of the kaiju and their masters is also very similar to Alternative’s BETA — though I’m pretty confident no one involved in Pacific Rim has read Alternative, so those’re almost certainly accidental echoes because both draw on similar influences.
One last thing that comes to mind: Stacker and Chuck blowing themselves up seemed to me rather un-Hollywood — I mean, that’s basically a suicide bombing! — and rather anime. But I haven’t seen enough Hollywood cinema to pronounce on that.
I could buy the no direct homages bit easier were it not for the Mazinger silhouette and Scopedog helmets, but I suspect del Toro felt those were fleeting enough not to be an issue. Also, good point about Cherno Alpha’s VOTOMs-style fist jolt – I saw that but didn’t make the connection.
Dying of mysterious anime disease is a classic, though I suspect that’s actually a reference anime takes from even older stories (beautiful, noble Shinsengumi members dying tragically young not from battle but tuberculosis. But I suppose it is pretty anime.
The main Gunbuster reference I saw (now that I think about it) is Striker Eureka’s chest missile array; the pilot’s make a motion as though they’re tearing their chests open to expose the missile tubes. Sadly I’m not very familiar with Getter Robo – I’ve only seen a couple of scattered episodes. Likewise, I only saw the first episode of Muv Luv (Alternative, I guess?), so I didn’t catch any references there – the kaiju masters’ agenda reminded me of the goals of Getter Robo’s Dinosaur Empire.
The sacrifice of Striker Eureka feels much more anime than Hollywood (Hollywood conventions generally don’t allow the rival to significantly exceed the protagonist in any significant way, at least in the long run) – at the least it reminds me of Kittan from Gurren Lagann, though of course that trope is quite a bit older than GL.
I’ve been trying to think of whether the dual-pilot setup is an homage to any particular show. Since the robots don’t combine and require the pilots to stay in sync I can’t exactly point at Getter Robo or even Gatchaman; the closest example I can think of are the Neuronoids from Betterman. Actually, Betterman also has the idea of somebody being able to tap the enemy’s psychic communication; maybe the Drift was inspired by the Limpid Channel?
When I mentioned Alternative, I was really thinking of the visual novel — the Total Eclipse anime doesn’t really treat the question of what the aliens are after.
The Striker Eureka chest-ripping is a good catch, I think. I have a feeling that Gunbuster’s ripping open the chest to reveal the reactor goes back to Getter Robo (Getter Ray reactors are wonderful impromptu bombs) but I may be wrong on that.
Betterman seems very recent and very obscure for an influence on PR, but you may be right — at least, the similarities are there, whether intentional or not. The control system in PR seems like a combination of something like the Limpid Channel and the motion-capture-in-a-big-room style of robot piloting in G Gundam.
I don’t watch very much Anime…But isn’t the quote “Who the hell do you think i am” a reference to the Gurren laggen thing or whatever its called?
Look closer Newtypes. When Becket is pinning pics to the wall in his quarters, notice the Sphinx-like face, a la Giant Robo.