Apple is likely to release the iPad 2 in April and an enhanced version of the iPhone 4 in July or August. It's not like Apple to do a wholesale redesign just a year after a previous one, so expect the next iPhone to be an improved iPhone 4 -- what I'm calling the iPhone 4x -- rather than an iPhone 5, just as the iPhone 3G S followed the iPhone 3G. Although Apple made huge strides in iOS 4.x in the past year, it still has areas where it should improve.
Here are the top 10 sets of improvements Apple should be working on for 2011.
A desktop-capable browser
If mobile devices are to supplant PCs for many tasks (I believe they will), they need to have browsers that can run the same apps as a desktop. Today, neither Apple's Safari nor Google's Chrome can make that claim. The iPad especially can succeed even more as a laptop replacement if its Safari could run the same Web apps as the Mac and Windows versions, such as Google Docs and Microsoft Office 365. Given that HTML5 is essentially owned by Apple and Google, either company could give mobile devices parity with desktops. Regardless of Google's actions, Apple should take the initiative.
Along these lines, I wish iOS would stop refreshing Web pages when come back to them after switching away. If the app has a form I'm filling out, I lose the data I entered (ironicially, I usually switch out to get a piece of requested information for that form). With its introduction, iOS 4.2 reduced the frequency of such refreshes, but it still happens too often. However Apple is deciding the duration for caching a Web page, it needs to be revisit that algorithm.
Multiple account support
Mobile devices are typically used for both home and work purposes, yet an iOS device is essentially locked to a single iTunes account. That needs to change, so work assets can be managed by iTunes at the office and personal assets can be managed by iTunes at home. This should extend to family use at home as well: With products like Apple TV and iTunes supporting sharing of content across a family's devices, there has to be a better way to manage that federated group of users and assets.