First of all, let me just say that I love Apple and everything it creates, so this isn't meant to be an Apple-bashing post. It's precisely because I use my iPhone and all it's handy capabilities so often that I'm bugged by these (mostly) minor issues.
Post your own iPhone pet peeves in the comments!
It irritates me to no end that when you open a link in a new window in Safari, you are automatically switched over to the new window without the option of staying on the page you were already viewing. This has bothered me for ages, but at first I kind of disregarded my ire, figuring it was just one of those stupid, pointless things that was never going to change. But then I got my iPad and found (to my delight) that in Safari on iPad, new tabs open without disrupting your current viewing! This needs to happen on iPhone, fast.
2. Downloading Apps from the App Store
Along the same lines, can someone please explain to me why on earth the App Store has to close every time you click download/buy on an App? I don't need to view my home screen! In fact, chances are, I want to keep browsing for apps! I almost always download multiple apps at a time and it is such a waste of time to have to watch the app store close and reopen after the purchase of each app. Unfortunately, I can't say this problem has been fixed on the iPad, unlike the Safari
3. Siri Lacking Support for Map Information in Canada
Apparently this is supposed to roll out in 2012... Fingers crossed! I want to be able to locate coffee (by voice command, of course) wherever I am!
But in all earnestness, this prevents you from viewing movie listings, searching for anything nearby you like a restaurant or post office, and looking up directions via Siri. These are all valuable functions, in my opinion.
4. Tweet from Siri
When I'm walking and want to send a voice command, I more often think of something that I want to tweet than of anything else -- and, guess what? It's essentially the only thing I can't do by voice command. Siri is great, but if they're going to integrate Twitter into iOS it would be really helpful if it were fully integrated.