In no particular order, these are the things I hate about iPhone after using for 6 months. I have an iPhone 3G with unlimited maxed out data plan via AT&T. 

1. Keyboard – The lack of a physical keyboard is particularly hazardous for me. The predictive logic is fine for normal people, but as a physician, shooting a quick email becomes an exercise in Gotcha when medical terms and abbreviations morph into correctly spelled but wrong words. I know this can be turned off, but this causes just as many headaches as leaving it on. Apple wants you to go to an Apple laptop for any heavy keyboard work. 
2. Battery Life -If you use it only as a phone, it gets through a workday. But if you use it as a smartphone, it barely gets through the day. Forget about an extended day, which is typical for me. This means carrying an external battery, cables, and adapters. I will gladly take some bulk for super long battery life. 
3. Lack of Memory Expansion -flash memory is now dirt cheap. You can get 16GB SDHC cards for less than twenty bucks. This is mind bending when you look at the micro-SD form factor. There is no reason for the iPhone not to have this except for the fact that Apple does not like hatches and holes and excessive buttons, and it wants you to upgrade when you tire of the lack of memory. 
4. No Copy/Paste -the lack of copy/paste is a philosophical decision on Apple’s part to avoid programs from contaminating each other via the clipboard. Every program runs by itself and tidily goes off when you turn it off. This fish bowl approach to tasking ensures that no program acts in a malignant fashion either intentionally or unintentionally. It’s Apple’s way of saying, “It’s a phone! Buy a Macbook for the heavy lifting.”
5. AT&T -Not completely happy with it, but I guess it’s a compromise. If you had to marry someone, but you lived in a village in the mountains in the Balkans and there were only three available women, four if you didn’t mind the one with no teeth, a glass eye, and a goiter, you make the best of it. AT&T is the oldest one of the bunch with large bosoms and behind to match. Sure you fooled around with the youngest one (Sprint), but everybody else did too -her biggest fault was inconsistency and broken promises. The middle sister (Verizon), the prettiest one, was also the most controlling. The way she smacked her other sisters around and barked order about how she wanted things done her way was not appealing. So you settle with AT&T. I find strange things happening with the new 3G network out here in the hinterlands. I’ll get 5 bars and a 3G symbol one moment with clear reception, and I turn my head and I get 1 bar with an E (for the slower data connection), and the phone call goes kaplooey. It happens in my car, in my house, in my office, outside with no obstruction whatsoever -and it is the Great Plains with no significant geographic barriers. But the oldest sister doesn’t care so much of your demands, understands if you fool around with the other two, and when drunk, take a roll with the toothless, one-eyed one with the goiter (T-Mobile)-after all -she’s got you now for at least five years from iPhone launch. 
6. No Bluetooth Anything -Polaroid recently asked TUAW (link) to post a generalized request to open up iPhone’s bluetooth for its portable photoprinter which works with just about every cheap-ass phone out there except for iPhone. This is a beef I have particularly when combined with complaint number 1 -no Bluetooth keyboards, no stereo bluetooth headphones with microphones, no Bluetooth printing, nada. Zip. Just the earpieces that go missing after a few days.
7. No Easy Way to Organize Your Screens -Apple happily lets you have as many screens as needed for the Apps you download, but organizing them is a disaster if you have more than one screenful of apps (I have seven). If you do factory reset or something like it, all the apps are jumbled. It would be great if you could do it on iTunes and save these configurations. Or if the home screen gave you a link to your productivity apps, your games, your casual games, your deep strategic games, your games to show off the iphone with, and your games that you play for hours on end. Also your photo apps and music creation apps. 
8. No Passthrough Internet -this is more AT&T’s fault than Apple’s, but I blame both since they got hitched up. You can with some phones, hook up your cell phone to your laptop and use its wireless internet connection to browse from your laptop. I did it a couple of times with my older Windows Mobile smartphones but it was a dodgy affair involving turning on and turning off various things and digging through control panels and hoping for a connection. It would be so wonderful to just attach the iphone and get it’s 3G connection as a connectivity option with no toggling or hoping. AT&T wants you to buy a separate data modem plan. 
9. No Video Recording -I know you can jailbreak to get this feature, but I don’t want to jailbreak. I want it now, no excuses.
10. Contacts choked -I have over 2000 contacts and also more via my Exchange connection to my office’s directory. This makes looking up contacts a frustrating affair as I wait often an interminable amount of time to look up a phone number. Absolutely unacceptable. Also, search is dumbfoundingly linear -you have to type the contact in the order that it was input. Sometimes, if I can’t remember a last name, I’m SOL. 
11. No wordprocessing, no spreadsheet, no Filemaker database access -this is so basic, and so missing, but also related to all of the above -no keyboard, no multitasking, no copy/paste.
12. No Flash, No WMV, no non-Apple media formats, No Java -this is cumbersome at best, and criminal at worst. I just don’t get it. Very few people use Quicktime anymore. I get the feeling that with Flash -Apple loses some control over the apps and games. 

This still doesn’t drive me away from iPhone because it really is the best smartphone experience. But I am not married to it, and will runoff with the next gadget that does fulfill my needs. And I got needs.