"I want to create a GitHub app for Mac OS X that will allow you to stay up-to-date on the latest activities of your friends and favorite open-source projects."
The activity stream is just not a good tool to stay on top of what's happening when you're watching hundreds of projects.
For instance, the GitHub wiki is actually stored within a git repo. Having a local editor/viewer built into this application for the wiki would be useful.
This goes for the ticketing system as well.
And finally, to have a git GUI built into the application would be useful, even at a simple file-browser/log-viewer level (as I would probably use the command-line and tools like Tower for any more complicated requirements).