I think engagement with content comes when someone who's accessed the information is able to question, discuss, and share that information. So for mobile content it would be building community, interaction and feedback into the delivery. Youversion are doing this and others.
For example look at the Foursquare app and somehow, despite the pointlessness I see in "checking in" to various locations - I enjoy doing it, have connections and competitions with other users around the world and locally, receive badges and mayorships for check-ins - all these continue to draw me into the application. There's probably massive marketing data potential but its invisible to me.
In ministry - we cant rule out facetime discipleship. Can a mobile app prompt those interactions where we are close enough to people to smell them? 8-)
Off the top of my head here's a few things:
First off, the higher the quality your content is and the more relevant it is the more likely you are to have people come back for more. Is your media truly enjoyable to the people it is meant for? The biggest draw for people watching video on mobile is apparently humor- would it be too un-Christian to add humor to our materials (if you ask me God has a really great sense of humor!)? Also, story/narrative rules compared to teaching/apologetics presentation.
Second, although we typically love to make sure to try and answer all the questions in one fell swoop, if you're really looking for engagement perhaps for every question you answer you should raise another. Entice rather than satisfy. The TV series "Lost" is a great example of this- it kept people hanging on for five seasons looking for answers to questions they never had until they watched the previous episode. Plan out your media as a series and always leave your viewer/listener with a hook that will draw them back for the next episode.
Third is, quite simply, making sure there is an obvious avenue for the listener/viewer to take to continue their interaction with the media, ministry, Church, etc. If your media does one and two but leaves no clear path for the person to access more and deepen their engagement then all is for naught. Do you have a website, SMS contact number, etc. given in your media piece?
Fourth, as CSmythe, alludes, there needs to be individuals and community available for the listener/viewer to engage with. Engagement with the media is great but engagement with the Church is the goal. If your goal is engagement make sure you have people ready to engage with those that have been drawn in.
Fifth, and finally, I'm challenged learning what is going on with "Transmedia". The idea behind Transmedia seems to be to create deep engagement through a very strategic/foreplanned integration of web, social media, video, mobile and gaming aspects into one's media project. I'm here at VSN site today to add to a previous post on the subject and I recommend you check out the links that were up previously as well as the ones I hope to post in just a few.