I won’t surprise anyone if I say I love my iDevices. I’ve tried many smartphones and tablets, and I keep coming back to Apple’s products, because the fit my mobile needs best.
“Best” isn’t “perfectly” though, and there are a few compromises I’d love to see revisited for the next version of the OS. Here’s my list:

• Background downloading
  I understand why applications aren’t allowed to multitask. Battery life, security, yada yada, I agree with all that. But I’d love to get a way for applications to silently download content even if they’re not active; RSS feeds, podcasts, emails, etc. It could be limited in different ways: only when the device is plugged in, or only once an hour per app, or only for apps that have been used in the past week… Or all of the above. Bottom line is, batteries are probably good enough now that if Apple allowed for a limited version of background downloading (not background processing), it would be more of a benefit than an issue.
  It works with NewsStand, I think it should be expanded a bit beyond that.
• Live icons
  By that I mean icons that can change to indicate different statuses. Again, it could be limited to preserve the aesthetics of the OS, and I’m sure Apple would check for every app that requests that Lordly privilege, but some apps could definitely use something like that: in some cases, having to launch an app just to get half a second worth of information is counter-productive, and there has to be a way to tackle that issue without compromising iOS’s advantages. I think.
• Third party Siri API
  Yeah, that’s an obvious one. I don’t know how it could even work and not make a gigantic mess of things, but being able to talk to different apps through Siri would be quite cool. Maybe with a limited set of commands per app? Or a list of app-specific keyword activator? Who knows…
• Facebook integration
  Another obvious one. I don’t use Facebook all that much, but honestly if you have Twitter integration, you have to have Facebook integration as well. And I’d love to get Google+ too while we’re at it, but I think that’s probably a bit less likely.
• Game Store
  That’s not so much something I want as something that might happen anyway: last Christmas, an official “Game Store” app was seen on the app store for a few days, before it was removed (and confirmed as a “work in progress”). So it might never actually come out, but with games trusting a huge part of all the apps lists and charts, it would make sense to put the them in a different store: games on one side, everything else on the other.
• Game pads, or official iOS game pad specifications
  Most gamers agree that smartphones and tablets could be genuinely great gaming machines… if only they could use a “proper” controller (tablets especially). They are getting fabulous amounts of computing power after all, and input seems like it is the only thing holding them back from “real gaming greatness”. Don’t get me wrong, touch is great for some games, it just isn’t ideal for all types of games. We’ve even heard ramblings about Apple playing around with experimental external game pads, and given the success of iOS gaming it’s hardly surprising they’re exploring the idea.
  Of course, apps would still need to be fully usable without the external controller, for compatibility’s sake and for those who don’t want the hassle of logging a controller around… But I would definitely get one.
• Proper stylus support
  That’s more of a pipe dream than an actual hope. It’s also more to about hardware than software, but what the hell, let’s be outrageous.
  We all know it: capacitive screens are great for touch and crappy for styluses, and resistive screens are crappy for touch and great for styluses. While the former is clearly the better choice if you can only have one, everyone would still love to be able to take notes and draw properly as well if it was possible… It doesn’t seem to at the moment, but it’s still in my list. Maybe an official standard for active devices would help adoption in apps? That’s unlikely to happen until Apple fully embraces styluses as well, and that’s unfortunately still a long ways off.

What I’m not so keen on:

• Actual multitasking
  Yes I know, as I implied in the previous list, I’m a heretic… Some of you probably think that multitasking is good, that it would solve so many problems and allow apps to do all sort of cool stuff.
  Well yes, multitasking would of course have lots of benefits. But it would also have dire implications for the system as a whole: processes running forever, slowing the machine and eating up battery, lists to plow through to make sure you don’t have something running that shouldn’t be, etc etc… If I wanted multitasking, with the good and the bad, I’d be using an Android phone. It’s good that iOS and Android are different. It gives us choice. I like my phone baby simple, and for now I think iOS doesn’t really need true multitasking.
• Bigger screen
  Again, we’re getting into hardware territory, but I’ll be daring.
  I don’t really think I want a bigger screen. Wait, scratch that, I’d love a bigger screen: I just don’t want a bigger phone. If they manage to make the screen larger (edge to edge?) without making the phone significantly bigger, I’ll go for it. But I don’t think I’d like a gigantic 4.5 inch screen if it made the phone bigger in the process. So until they find a way to make that physical conundrum work (foldable screens!), I’ll by happy with my “small” iPhone.
  Oh, and while we’re on hardware: I want my phone to be thinner and lighter too, but I would go for “same size and weight for more battery” if that was the choice.
• 3D anything
  3D is crap. Cameras, screens,  all of that, I don’t care for any of it. It might be just me; I have a very hard time seeing the 3D most of the time, and at best it attains the level of “not too annoying”. Maybe there will come a day when technology makes it awesome (and not headache inducing), but I haven’t seen that yet. For now, 3D is a no-no for me.

I think that’s it for my list. Anything I forgot?