Just a few errors I noticed:
The end of Italian East Africa is generally considered to have come in May 1941 with the surrender of the duke of Aosta. Though various small guerilla groups continued to fight in the hope of a German/Italian victory in north Africa, it cannot really be said that Italy controlled Ethiopia or Somalia after May '41.
Madagascar and French West Africa were definately still loyal to Vichy at this time, so placing them under U.K. control is completely wrong. If simply making Vichy German, as this map does with French North Africa and France itself, then the same must apply to the other Vichy held colonies.
Netherlands colonies (DEI) to U.K. is reasonable, but Iran is incorrect.
The Anglo-Soviet invasion was in August-September 1941, so the map is wrong for June/July (Iran was then still independent). Even for December it is incorrect, as control and occupation of the country was divided with the U.S.S.R. controling the north including Teheran, the British occupying the south. On a map that divides Iran north/south there really is no excuse for not representing this.
Calling southern Libya Fezzan is correct, but really this was just desert and should be part of the Sahara.
FWA covered a much wider area; the territories here would be more accurately called Senegal and French Soudan.
FEA should be Chad.
Congo is wrong, this is Ubangi-Shari, later Central African Republic/Empire.
“Bangladesh” should of course be East Bengal.
“Dutch East Indies” should be Timor, or “Flores islands”.
Bonin islands and Iwo Jima hardly justify two territories.
As I mentioned, Volgograd is the post Stalin name for Stalingrad so is a complete anomoly.
Caucasus generally refers to the region named here as “Georgia”. It would be correct to call the northern area “Ciscaucasus” and the south “Transcaucasus”, but I prefer to apply Caucasus soley to the southern region based around the Caucasus mountains. The north migh be called “Terek” after the major river running through it.
Nova Scotia is not an island but a penninsular of the Canadian mainland.
Can’t imagine what that large island off the coast of Wales is; Atlantis?
I do not care for the ambiguous usage of, for example, calling one territory “France” and then another “Western France”. Each should be distinguished individually from the whole country.
Baluchistan bordering Uzbekistan is wrong; the British and Russians deliberately drew the Afghanistan border across to China to prevent there being a Russian/Indian border.
Yakut does not border Mongolia or China.