I was recently doing some work with a group of trainers who wanted to get to grips with using Moodle with mobile devices. Their group of learners are using mobile devices - often as their first point of contact with the Internet.
So I recommended that we try out the Moodle App.
This was largely unsuccessful since quite often the app dropped the user back to the browser to carry out particular interactions eg: uploading a video created on the phone could not uploaded without going to a thr bowser, logging into the website (rather than the app) and then uploading in the browser.
This was quite counter intuitive. The group suggested that, at the very least, the app should pass the user credentials onto the browser to avoid having to log in a second time.
Also, the sudden change in theme from the app to the website was misleading and confusing. Perhaps a mobile theme is needed which matches the app interface...
Hope the feedback is helpful.