Pinch/Zoom on the home screen. The app pages could be zoomable via a pinch motion, that would allow easier organization, and more icons on the screen.

Sorting of apps on the home screen. “Genius” could sort (when invoked. Not automatically.) by app usage, so apps used the most appear on the first screens. Sort by name. By date downloaded. By App Store category. Even by “set” which could save and recall groupings of apps together. Even a flyout folder similar to OS X’s Dock stacks for grouping apps together.

Notifications. I like TUAW’s idea of a notifications screen that is available via vertical swipe from any page on the home screen. A notifications app could be an alternative interface to that screen, with its own badges, and the app could allow for filtering push notifications, or suppressing push notifications to a badge on the notifications app (plus the app that actually triggered the notification). Apps will need to be rewritten to support this feature. The notifications screen would have Growl-like bubbles showing the app and a line or two of the message. A tap would open the app, or, at the app’s discretion, even allow a the bubble to expand to a larger preview. And some new notifications: Alerts from the Weather app, upcoming calendar events, App Store updates. Allow frameworks like OpenFeint or Plus+ to hook into notifications as well.

More refined notes app. Take a look at the Newton’s notepad app. Categories, support for free-form drawing and shapes (make something close to a triangle and it will snap to a triangle), customizable “stationary,” even mini-fields that turned it into a flat field database. Not anything to challenge Bento, but more structure than just a free form list. Also look at Notational Velocity, a wonderful, very simple app for Mac OS X in which you search for notes and create notes at the same time — the search bar turns into a title field once the search string fails to hit on an existing note. Simple, elegant, clever, and very useful on a iPhone-sized UI.

More refined Weather app. In addition to a live icon (the fact that this isn’t already the case borders on a bug), the Weather app should use GPS to get the weather for the current location automatically, include radar maps, and have notifications for severe weather alerts.

Wifi/Bluetooth syncing. Along with iTunes 10, the iPhone should allow for “mini” syncing over Bluetooth (updating IMAP/calendar data, play count for media files, pushes) or full syncing over WiFi.

Bluetooth Mac remote. Basically the features of the excellent TouchPad app, over Bluetooth.

Better support for A2DP. Those of us with advanced Bluetooth headsets, as well as Ford Sync users, demand it.

More informative lock screen. I don’t think we need to go full widgets, but would a “live” calendar and GPS-based weather display really kill you? Or a few lines from the Notifications app?

Integrated web search; open search API. One thing Palm’s WebOS gets really right. Start a phone-wide search. When there are no hits from the internal database, make the assumption that the search should go to the web and offer choices for the search provider. Google and Wikipedia are good starts, Bing and Wolfram|Alpha would be very nice too. Allow app developers to hook in to this, so (say) IMDB could add their search to the list. Searches added by apps open up in the app rather than Safari. Allow a preference pane (or even a dedicated search app) to allow the user to filter and order the search engines. Also, apps could make their own databases available to search.

Desktop display mode/app. The iPhone should be have a mode or app that activates when the iPhone is docked and oriented landscape. This could be a desktop calendar, showing a monthly calendar on half the display plus notifications or day calendar, just a digital clock, only notifications, currently playing track with controls, etc. There should also be a night clock mode, with a dark digital clock display.

Full suspend/resume. If multitasking isn’t an option (and I tend to agree that the UI to make this truly simple and elegant isn’t there yet), it can be easily simulated by full support for dumping application RAM into storage and doing a complete restore when the app is resumed. For 3GS and 4th gen hardware, there’s probably enough RAM to keep the last app in RAM without having to dump it to storage, making it even faster. But suspended apps don’t get any CPU time, keeping battery life high.

Integrated chat & SMS messaging. The WebOS can seamlessly move a conversation back and forth between GTalk and SMS. It seems simple enough: contacts have both a chat name and a SMS phone number. The threaded, bubbled, iChatty interface for SMS messages could be extended to switch to Google Talk or AIM if desired.