This weekend idea is much simpler: Turn the iPhone home button into a tiny LCD screen so it can display context-sensitive information.
This is the problem that could* be solved:
So for example, there could be icons to end a call, cancel an operation and go backwards (or forwards) from your current position. It could also display the Apple logo when in sleep mode, a progress bar when updating and probably much more.
Thinking about it as a secondary display, it could probably be used to display some useful information that you may want to keep an eye on while performing another task, like the time and battery life while playing a game or using another fullscreen app. As a smaller screen, it could also be a useful place to display information without having to keep the main screen active, like a timer countdown, progress through a podcast, unread email count, signal strength etc.
And when you simply have the option to return to the home screen, the original icon can be displayed:
Unlike regular onscreen buttons, this one would have the advantage of still being a hardware button, so it would remain responsive even under circumstances when some software is hanging.
I’m certain Apple (and many others) have thought of this already, but I still think it would be a cool feature.
* Note: Could be solved! I haven’t actually brainstormed and reasoned this out as well as the last idea, so there may be many excellent reasons not to do this (besides production costs, etc.)