The fact that I-401 is carrying around a Wave Motion Gun normally reserved for at least heavy cruisers (hers came from a battleship, even) became less of a surprise if you dig around a bit in The Other Wiki. The I-400 class of Japanese subs are the largest submarines of the WWII, and continues to be the largest subs ever built until the Soviets build their nuclear-powered behemoths in the 1960s. They are capable of circumnavigating the globe one and a half times on a full tank of fuel, and actually closer in concept to a submersible aircraft carrier (granted, their planes are ambhibious). Couple that with the advanced powerplant Fog Fleet has and the fact that 401 doesn't have any planes with her, that means there is enough room and power to store and (barely) operate the Wave Motion Gun.
Despite the US Navy's large presence in WWII, especially in the Pacific, no Fog ships based on American vessels have been seen yet. Why is this so? One possible explanation is that, since America is one of the few (if not only) countries to retain most of its military power and industrial capacity, the American branch of the Fog Fleet is concentrated more in the Eastern Pacific and Western Atlantic, keeping the US Navy at bay. This is confirmed in Episode 11, as a Fog task group made up of American ships arrives to interdict Iona from reaching Hawaii.
Kyouhei: Oh yea, that reminds me. Why are all of you Mental Models girls? Aren't there any guys? Iona: Huh? Kyouhei: No, don't "huh" me. Aren't there any guys? Iona: When you humans leave official records of ship, don't you all use feminine pronouns for ships? Aren't ships female? Kyouhei: Huh? Iona: Don't "huh" me. Kyouhei: (sweat drop) Is that all there is to it? Iona: Yup.
Why does Haruna always seem so meek and feeble whenever she loses her coat, as opposed to the indomitable mountain of a person she usually is with it? Don't forget, that coat is pure nanomaterial, which, unlike other nanomaterial clothes, is fully capable of tanking hits from infantry! She probably feels far more naked without it than one would normally assume, because it's a shield to protect her body, as well as her modesty.
Also the fact that, well, she doesn't really wear much under it to begin with until later into the story.
This trait is anime-only and an exaggeration of her first meeting with Makie when Haruna was disorientated and out of her depth. She's worn the coat less and less as the manga has progressed.
Nobody drinks coffee. A very subtle example of Shown Their Work, as Japan doesn't grow its own coffee and importing any via rocket would be very low on the priorities list. Everyone drinks tea or some other beverage instead. The singular exception to this appears to be Lexington, but she's probably just synthesizing it from nanomaterials anyway.
Judging from the imagery from the mental chatroom in episode 11 and the fact that the Corrosion Torpedo hit on 400's sail/fin (thus most likely hitting her right on the control room)... Did Gunzou just obliterated 400's core?
In the anime, Takao sacrifices her physical body to reconstruct the I-401. However, considering she still retains her core and processing power, there should be nothing that prevents her from reconstructing a physical body. It wouldn't take a lot of nanomaterial for that, and the Ars Nova should have at least that little extra to spare.
Why not just go to China? Seriously, it's a fraction of the distance, and it's got a land connection with India, Russia, Europe and Africa. Several decades is more than enough time to build up some pretty impressive overland trade routes.
China was discounted as a producer of harmonic torpedoes because it was devoting resources to intervention in the European conflict. Continental Europe (including Russia) is busy setting itself on fire in an unusual repeat of World War I while Britain is even worse off than Japan (somehow). It's pretty much America or nothing.
This is still no answer, why they don't go to Sakhalin and from there, after crossing continental Russia, continue via the Bering Strait (which is frozen occasionally and thus can be crossed without even using ships) or the North Pole to the U.S.
There exists no infrastructure. The roads up past Mongolia are poorly maintained, and sometimes don't even have bridges. Eventually, there are not even any roads period, so it is literally impossible to get there. Even if you did, you'd still need to get a ship to the Bering Straight anyways, and then what would be the point at all?
Also note that with the exception of China and Russia (both discounted as explained above), America is the closest country able to produce the weapons.
England apparently hasn't changed socially since the Edwardian Era in the manga; the country apparently still relies on the aristocracy for leadership and even fashion appears to be terribly old-fashioned.
The 20 meter rise in sea levels that feature in the backstory are notably absent from the London scenes: Chihaya Shouzou and Musashi have a conversation in London's Hyde Park, which is low enough in elevation for their park bench to be underwater at high tide; Buckingham Palace would be entirely flooded even at low tide.
The Channel Tunnel linking Britain and France should still be running. Both terminals are either above the 20 meter waterline or could easily be protected from water. There's no reason the two nations wouldn't be connected unless the Fog deliberately destroyed the terminals (which goes against their general ban on attacking land targets) or if one or both countries cut ties deliberately (equally unlikely given the volume of trade that goes through, a naval/air blockade would make the tunnel of vital importance).