This is something that may well come in stages. There will be new, official-but-optional apps from Google, Yahoo, or other partners, then a developer program, possibly with a high barrier to entry, then a free for all much later.
We should be seeing some refinements to the iPhone OS shortly. The one I'd like to see first: some form of copy and paste. It's sorely lacking. This is the first handheld computing device I've ever owned that comes close to really letting me do my work when I'm away from home. I can keep up on my email, and browse the web on a real-ish browser. But if I want to grab a URL from an attached document and send it in an email? Better have a pen and paper handy and don't leave out any slashes or ampersands.
Lack of search is also a big problem. I like to put people in my address book, and sometimes they're people that I do business with, but I don't know very well. Sometimes I'll put notes in (and this is possible on the iPhone) about them so I can remember who they are and why they're in my contacts. So I'm trying to remember the name of the guy who services my vacuum cleaner. No problem, I'll just search for vacuum. Or not. The iPhone has no search.
The lack of search would be especially acute if I were to keep a bunch of documents on my iPhone that I needed to search through. But, what? The iPhone has no method whatsoever of uploading, categorizing, managing, reading, or editing documents at all, other than as email attachments? (and the iPhone can already display various types of documents, like word, excel, PDF, and images) You have to be kidding! With all that potential disk space? Alas, it's true.
The calendar is nice, but lacks functionality. It needs a nice to-do list function, if only a mimic of the Mac's calendar app to-do list. It should also allow for over-the network shared calendaring, like the Mac's.
Finally, there are some small tweaks that could be made while using the phone features to make it a bit harder to accidentally start calling someone when you're using the address book. Some of the routine navigation requires you to alternate between pushing things on the top and bottom of the screen. But aside from copy and paste, the OS is very refined for a 1.0.
Several of the included apps should see a bit of refinement and some additional features. I really miss the ability to open a link on a web site into another tab. Especially when using EDGE, it's really no fun to leave the site you're on when clicking a hyperlink, twiddle your thumbs for thirty seconds while it loads, then go back and reload the page you were reading before. I use my iPhone for heavy web page reading. I browse the web while waiting in line, while eating, while my kids play at the park, even while on the toilet, just like a newspaper. And Flash would be nice.
The iPhone does a bit of caching, with Google Maps and Safari, but, especially because of slow EDGE performance, it should do much more. Currently, if you leave Safari for more than a few seconds, it forces you to re-load your pages, even in the active tab. I can think of no reason why the data in all your tabs shouldn't be cached indefinitely. The same goes for the last active Google map, and various surrounding maps and zooms as well. Often when accessing an email with attachments or images, the iPhone seems to want to re-download this content before I can view it. If I have gone out of network range, I'm out of luck. This should not happen.
Last but not least, the iPhone lacks MMS. Its SMS app is very nice, but sends only text. This will be rectified in an upcoming software update, I'm sure.
In Conclusion, things we'll be seeing very soon in iPhone software updates: some expansion of available apps, copy and paste, search, document editing, file management, Safari, Calendar and Mail enhancements, Flash, MMS, and better caching.