Update 2011-06-08: Several of my wishes have been fulfilled.
There are still enough things on iOS that add up to make it the best choice for non-technical people who just want a hassle-free experience. But, the competition is improving and bringing out tablet-specific editions:
Android Honeycomb has many user-interface innovations and improved looks.
WebOS apps can now also run in a browser (and probably as stand-alone desktop apps before long).
There are four instances where Apple is the one doing catch-up and needs to improve iOS (listed in order of urgency).
Bonus: Four more gripes.
Notifications: Having your workflow interrupted by a notification is unacceptable. With email, there can often be several of those interruptions, which is quite annoying.
- There are multiple things that need to be managed as notifications: long-running tasks (music playing in the background), status (device currently connected to a desktop computer), incidents (missed calls).
Getting Notified: Gives an overview about how various mobile operating systems have implemented notifications.
Independence from PC: Why do I need to connect my iPad with a cable to a desktop computer before I can get started? Syncing is also an unpleasant experience.
- Changes will probably come soon, as Apple is rumored to improve Mobile Me . Steve Jobs has already promised wireless syncing.
- Tim O’Reilly makes a similar observation on Twitter:
If iPads are “post-pc devices” why must I sync with iTunes before I can use one? $GOOG gets "post-pc," $AAPL doesn't. Link: 
- Some cloud-syncing can already be done on iOS .
Faster web browsing: This is one things where my iPad reminds me most that I’m not using a desktop computer. There must be a way to make switching between open tabs faster, e.g. by caching in Flash RAM.
Universal file system: Currently it is difficult to group files across applications (e.g. by project) or to work on the same file in different applications. A universal file system with Drop-box-like syncing  would help with many workflows. Maybe Apple could also innovate a little and support tagging for files. A file can only be in a single folder, but could have multiple tags, for example “holiday”, “paris”, “2004”. With folders, you have to decide whether to organize by topic, location, or time. With tags, you can do it all at once. Lifestreams  are an excellent example how you can add power to a file system without making it more complicated.
GoodReader is currently the closest thing to a universal file system. It offers file management, can send its files to applications (like Dropbox), can receive files from applications (unlike Dropbox). It also syncs files via iDisk, Dropbox, SugarSync, WebDAV, FTP, SFTP. Thus, you can sync with your own server!
- iPad virtual keyboard. An additional row in the iPad’s virtual keyboard. WebOS has that and its great not having to switch levels back and forth to type parentheses around something.
- Configurable preferred web browser. As long as Mobile Safari does not support tabbed browsing or file downloads, alternative web browsers such as iCab Mobile will be a necessity on the iPad. If I use such a browser, I also want links (e.g. in an email) to open in it and not in Safari.
- Taking pictures on the iPhone. Currently, it takes too long to go to the camera app and to take a picture via the awkward virtual shutter button. There should be a shortcut for the former and the ability to use one of the hardware buttons for the latter.
- Support for multiple users. iOS devices do change hands frequently. If I borrow one of mine to another person, it would be nice if I could add an account for them. Then there wouldn’t be a risk of them causing damage and they could come back to their previous environment, later on.
These are currently my only major gripes with the platform. I don’t mind the limited multi-tasking, because it has been implemented very well and saves battery power.
- What if Apple made MobileMe social and gave everyone an account?
- If iPads are “post-pc devices” why must I sync with iTunes before I can use one?
- Cloud-sync your iOS calendars (bonus: PC/Mac)
- Information management classics: Lifestreams (1996)