I wrote a longish Quora answer some time ago on the topic of why it was taking a long time for Asana to deliver a great mobile app with offline functionality: http://www.quora.com/Asana/Why-is-it-taking-months-for-Asana-to-deliver-a-native-mobile-app-with-offline-support
Even though pretty much none of there remarks were taken into account in the new version of Asana's mobile app, I was still hopeful that the new version would bring much needed usability improvements: http://blog.asana.com/2012/09/our-iphone-app-levels-up/
Unfortunately, this new mobile interface still comes short on a large number of points:
* Unexpected bugs (I tweeted about one last week that prevented me from using the app)
* No way to see the details of a priority heading (right I'm stuck not being able to access a link I know I stored in the "Notes" field of a heading)
* No search (!)
* No way to assign a task to more than one project, nor to move it from a project to another (which kills severak if the workflows I'm using)
* Clunky navigation (switching from a task in a project in a workspaces to another task in another project in another workspace requires a lot of taps)
In their blog post, the Asana team states that "Our ultimate goal is a mobile experience that matches the craftsmanship, elegance and power of the desktop web app. We think this version gets a long way towards that goal, and we hope you agree!".
Let's agree to disagree.