1) Better signal reception. I live in a rural area where the mobile signal is variable at best; though it's possible to get a signal in the kitchen standing at the end of the table, moving a few inches to left or right can kill it to zero. When I've tried Samsung smartphones and non-smartphones on the same network in the same location, they seem to handle it fine.
2) Longer battery life. Of course, everyone says they want this, but the iPhone is again not a great contender. The iPhone 4S in particular hasshorter standby battery life than the iPhone 4, for reasons that have never been explained (though might be due to the heftier CPU). Certainly I've found that after a day consisting of a couple of hours' music listening, in parallel with a few hours' email, web and app use plus some phone calls, that the iPhone falls gasping across the threshold as you arrive home.
Other makers (Samsung again, and RIM's BlackBerrys, and to a lesser extent Nokia's new Lumias) do better here. Perhaps the addition of an LTE capability with a larger screen (both anticipated) will mean a bigger battery capacity – so that if you're not using 4G, you'll get more battery time. I certainly hope so.
3) Android's "pattern unlock" system. Since I first used it on the first Android phone (the G1), I've liked this system enormously. You have a 3x3 grid of dots: you swipe a pattern (which you decide) to unlock it. Much quicker and easier to get right than numeric pins you type in. Obviously, to offer this Apple would have to license the patent from Google – and that's unlikely to happen in a hurry.
4) A "scripting language" to tie together multiple functions. Sometimes you want to turn off your Wi-Fi or turn off your 3G at the same time that you start a new app, or set an alarm for 15 minutes' time unless you receive a phone call, or any number of combined actions. That's when you need to be able to chain together functions from different settings or apps. Desktop OSs have this (Apple has a language called "Applescript"), and Android has an app that uses it in the form of Tasker. As smartphones get smarter, we need to make them simpler to use by putting programs together.
There are some signs that Apple is doing something like this, with apatent on a system to change smartphone settings by location, but that falls a little short. Also, the strings of actions you want to trigger aren't necessarily location-dependent; it might depend on time, or battery level, or location.
5) More control of phone functions using Siri. Though everyone was dismissive about Siri when it was introduced, I have found it increasingly effective: having a phone with a multi-digit numeric lock means that it's often faster to tell Siri "Tell X I'm on my way over" and have that sent as a text message than to unlock the phone, go to the Messages app, type a name and type a message. I can also walk while Siri does the hard work, which means I get there sooner.
Voice control is surprisingly liberating once you start using it enough. Get a pair of headphones with a mic and you don't have to take the phone out of your pocket.
But what's missing is the ability to use Siri to turn functions such as Wi-Fi on or off, or to launch apps (you can launch apps in iOS6), or trigger a chain of actions created by your scripting language as above. (Obviously you'd want to block: "Siri, factory reset.") There's a whole landscape of voice-controlled potential out there just waiting to be used.
6) A bigger screen. It's not that high on my list, but it's definitely a good thing in a phone. In time I can see phones becoming more like Samsung's Galaxy Note with its 5in screen: you control it mostly without having to see it (by voice), and then bring it out when you do want to interact with the screen, which because it's big offers the best interaction. Samsung is definitely on the right track with the Note.
7) Better use of colour to indicate status in the status bar at the top of the screen. At the moment they're monochrome; but it would be useful to know whether the phone signal is strong or weak through coloured bars (red, orange, green) as well as the number of bars; ditto for Wi-Fi and battery. It means at-a-glance understanding of what the phone's state is.
8) Less intrusive notifications. The introduction of notifications in the status bar in iOS5 (which people say copy Android, but are actually much more like Palm's webOS – because the engineer came from Palm) is great: it's a very quick way to find out what's new. But they have an annoying habit of covering navigation elements at the top of any onscreen page.
That means that if you're in a hurry and haven't been using your phone and have a lot of notifications, they keep rolling over the element and getting in your way; you have to flick them out of the way like flies, and there's a high risk of hitting a notification instead of an element, and getting yanked over to the notifying app. This is really annoying. Perhaps a larger screen will solve this by putting more space between status bar and the onscreen elements. Here's hoping.
9) 4G/LTE. We know this is coming, but it would be good to have the option of the superfast speeds it offers, even at the cost of burning through one's battery in an hour or so.
10) Wireless charging. Nokia got here first with the Lumia 920 (and HP before that with the TouchPad tablet). It is indubitably cool to be able to dump a phone in a cradle without attachments and then grab it up when you need it.
Update:one remark on Twitter was "it appears a 'Samsung Android' already answers a number of your iPhone X requirements". That's true except in one key area: user experience. In my opinion, the iOS experience is better than Android in lots of subtle ways that cumulatively all add up. Samsung's TouchWiz slows phones down (to give juddering scrolling); HTC's interface is the nicest I've tried.
Update: Android's notifications in Gingerbread, still the most widely used Android OS, aren't as informative as those on iOS5; they don't have content, just the fact that you have a message. Android 4.x does provide more detail in notifications.
Things I'm not expecting to see in the next iPhone