A comment from John Dexter had me thinking even more about the Twitter problem. I think it is clear to me, more than ever, that owning the platform is more important than owning the interaction when it comes to Twitter.
In 2012 Twitter decided it was going to be an app company instead of a platform company. They blew off their third-party developers in hopes to bring all of the eyeballs from the Twitter stream/firehose into their own app and webpage to monetize with advertising. This essentially laid the groundwork for Twitter not owning just the platform, but owning the entire experience. In the case of Apple and Facebook, this is good because it is their core competency to own all the widgets. When looking at Twitter, a big reason they are where they are today is because of innovations by third-parties. They would not be in mobile if it wasn't for other developers getting there first. All of the app innovations have been made by third-party developers, so much so that Twitter had to purchase one of them to catch up.
Twitter should take a step back and develop the platform to generate revenue. If agreements were laid out to developers allowing them to get a piece of the ad revenue generated through their apps, they would be great partners in pushing the ads in new and intuitive ways. Twitter can then focus on knowing the Twitter customer, the logged in user, better than Facebook knows their customers. I believe Twitter has an advantage because they know peoples interests better. The people I follow on Twitter align more to my interests than the people am "friends" with on Facebook. Facebook tends to focus more on real-world relationships and the close knit social graph.
Once Twitter can repair the relationships with third party developers and focus on developing the platform to maximize ad placement, they don't have to worry about innovating apps that sit on top of that platform, which they are not particularly good at doing anyway. This model would bring the most app innovation, while at the same time, allow Twitter to focus on revenue generation for the platform. The third-party developers would have to share all the data back and then Twitter can be the master of the customer, which is where the ad revenue will come from. Focus on being able to deliver the best ad to people consuming the stream.