Not having got the game, but having seen it played (and read all about it with the aim of getting it sometime soon) my initial impressions have been as follows. Most of them touch on things people have already said, but there are a couple of things at the end I don't think other people have mentioned that I thought I'd throw into the mix.
Whilst initially disappointed there were just four AOs in the game (as a fan of the King of Yellow I was disappointed Hastur didn't get a mention, but I was as much surprised as disappointed that Nyarlathotep didn't make an appearance) I can see why. Aside from Nyarlothotep, I figure they've gone with the four most influential figures, the most powerful of the Great Old Ones and the three central Outer Gods that arguably rule over everything. Azathoth, obviously, not as influential in human circles, but he's pretty central to the worship of other creatures, including Cthulhu himself, and it seems to make for an easy introductory scenario, so that's good enough to warrant its inclusion. In essence it looks like the main game has a lot of generic themes (but then I haven't seen exactly what monsters there are to pick from aside from a few... it looked like there were a lot of cultists).
I'm glad to see Nyarlathotep will be getting the next look in though - using the famous Masks of Nyarlathotep RPG supplement as possible inspiration it makes perfect sense that they'd produce something that goes beyond the simplicity of the basic game to cover him and his various masks. I imagine Masks will translate into various Epic Monsters - it'd be nice to see them each lurking around the parts of the globe the source materials original set them in.
It goes without saying that I look forward to seeing a Hastur/Kingin Yellow themed one too, hopefully one that acknowledge the King as a Herald to Hastur from the beginning, rather than to whichever AO is in play. The Tatters of the King RPG supplement does a similar thing for Hastur as Masks did for Nyarlathotep, although on a smaller scale, so I can see lots of option for a Hastur based game.
I agree that the game should probably have boosters that are based around particular AOs, so you can tailor your EH game to whichever AOs you enjoy. Whilst I think it'd be great to add totally new AOs to the mix, I think it'd also be great if Yog Sothoth, Shub Niggurath and Cthulhu (I less bothered by Azathoth, as I think it has a pretty simplistic goal that works fine as it is, and no really organised cult to speak of) had their own boosters to enable you to take their basic game to new levels or in different directions. And, as I've said in regards to making Masks haunt specific parts of the board, it'd be great to have AOs that acknowledge their ties to particular countries or continents (all those Severn Valley AOs, for example).
As well as additional cards I wonder if the new monsters that are added are kept aside, and only used to seed the mix of monsters whenever a certain AO has been chosen. So, for example, you'd get more Deep Ones drawn in a Cthulhu game, or more Byahkee in a Hastur game. This would definitely add to the inherent theme of each AO. Is this sort of thing covered in the base game?
I briefly mentioned the Heralds from Arkham Horror above - I wouldn't be against some sort of return of Heralds in EH. However, having just read about Relic: Nemesis this morning, I was wondering about the potential of having games where one player IS the Herald, able to play a game against the investigators. Like Fury of Dracula, but with Nyarlathotep. I'm not sure exactly how you'd implement that, but it could potentially be pretty awesome (and, again, help make EH a very different game from AH).
Extra boards? Whilst I can see the argument for a new board with a better representation for specific cities, I can't see that coming any time soon. The only possible new board I could see would be if they were to create an entirely new board for The Dreamlands, and that's a whole new can of worms.