The governments of this Earth are also limited in their interactions with magic-users. Partly, this is due to a lot of major governments having cultural, religious, or philosophical issues with magic. A larger reason is that a curse was placed on the governments of this world at some point in the past, making them reluctant to bring magic-users directly under their control, and thus, responsibility. Offering them consulting positions on some projects, yes, encouraging them to join a Society sponsored by the Justice Department, sure, but assuming direct responsibility for those loonies? Not a chance. The curse is more than just mental, having a probability effect, as well. This makes the victims less likely to try to resist, and less likely to succeed if they do, along with making people they communicate with less likely to say anything that would make the victims try to resist, or less likely to be heard (or listened to) if they did.
In terms of secret identities, if someone had one in the comics, chances are that the 'civilian' ID that we know is wrong: A Superman, but no Clark Kent, a Green Lantern, but no Alan Scott (though he has the same look), a Bat-Man, but no Bruce Wayne, and so forth (Ted Knight didn't wear a mask, and didn't have super-speed to blur his face, so I'm assuming he didn't bother to pretend he wasn't Starman; the 'magical' nature of the Gravity Rod explains why he's the only one using it, as it works poorly, if at all, for anyone else, and serves to frustrate him, since he's a Western weird scientist). In general, this Earth has a scary number of what we would call fictional characters. The sons of Holmes and Watson run a consulting detective agency at Baker street, Reed Richards and Ben Grimm are in the newly formed US Army Air Forces, Victor von Doom (probably not his real name) is in Tibet, and Erik Lehnsherr (Magneto) is in Auschwitz, learning hatred and madness from experts in the field. While there are a lot of Mystery Men, though, the number of people with actual
superpowers is quite low - there are many sorcerers and alchemists, but very few who could rationally consider a normal 2012 infantry squad/section (or one from 1940, for that matter) to be a non-threat, and most of
them could be taken out by a well-prepared ambush (mind you, killing Solomon Grundy is sometimes a
bad idea). The number that could reasonably expect to defeat a normal infantry squad or section alone is much larger, but there is a wide range between 'can usually defeat them' and 'they aren't even a threat.'
Overall, the human population of this Earth includes over a million extra people, compared to our 1940. That doesn't count the various other sapient species, like the Deep Ones or the
Mangani. In total, that's another few hundred thousand people, of various types, including some unique ones like Kal'El. Note that those Marvel calls Homo Superior (mutants), and DC calls Metahumans and Homo Magi, are
not a separate race or races, they're just humans with a strangely Lamarkian meta-gene complex that encourages a wide variety of psi powers. There are also an uncertain number of plant and animal species on this Earth, many of which are in danger of extinction, and some of which are psychic/magical.
Observation of the 'dark' side of this Earth's Moon (or more accurately, the side facing away from Dp-Earth) shows that several craters are covered by reflective domes, with smaller domes around them. When the 'dark' side truly
is dark, the domes become transparent, and well-lit cities and not-so-well-lit farms and forests can be seen within them, inhabited by Green-Skinned Space Babes in metallic clothes of varying degrees of skimpyness (or existence, in some cases), along with clunky-looking service robots. Contrary to the trend in Star Wars and Mass Effect, these space babes have hair on their heads, rather than being bald-with-eyelashes; Miss Martian's preferred form would fit right in, other than 'wearing' more than the locals usually do. Likewise, they're not all green, but green appears to be the dominant colour - or at least, they're usually the ones with the whips, and the other colours are usually the ones in chains. Travel between the cities appears to be accomplished by monorails enclosed by the same material as the domes, or for more remote cities, by vehicles that resemble giant silver golf balls, each with an antenna extending from the top like long, black thread; these vary in diameter from about 4 metres (13 feet) to a bit over 50 metres (165 feet). All is not well in the Lunar cities: apart from the apparent slavery that's been alluded to (which could just be judicial punishments or mainstreamed BDSM, for all we can tell), some of the robots appear to be broken down and not repaired, several cities have power going in and out in places, and a few domes have been shattered, mummies visible within. The lack of men, or for that matter, women who appear to be younger than about sixteen, or older than about thirty, is also suspicious. They don't appear to use radio, or at least we're not picking up any transmissions from them, but they certainly have telescopes, most of which are pointed at us.
This Earth will be the one of greatest concern at the start of the new era, because they have a demonstrated ability to reach us, and they have a Nazi Germany on the rise - and it's not like that can be kept secret, when anyone with an AM radio, some wire and household junk, a little technical knowledge (available online, or at your local library) and at most a visit to Radio Shack, can build a good enough radio telescope to listen to them, and only a little more would be required to watch their TV; pretty soon, there would probably be YouTube channels for it. Israel is not the only nation contemplating the nuclear option to deal with Hitler, and in some cases, Stalin. Those considering biological weapons might need to be reminded that this world's Superman is likely to be immune, does not have an absolute code against killing, and if everyone else died, would have access to Dr. Fate's helm and Green Lantern's ring.
TL;DR: Dieselpunk Earth, in 1940, with elements of the Wold Newton Universe and some magic, supers, & potential supers.