Here are two videos from Ali and his team who produced the native, paid iPhone app, mTouch (or MoodleTouch). The first video showcases the process of logging in and accessing courses, the second accessing and using the chat activity.
Additionally, mTouch 1.3 was recently submitted version 1.3 of mTouch to the App Store. The upgrade will be available shortly.
For more information visit http://moodletouch.com
Video 1 direct link: http://www.youtube.com/watch?v=4u_dPmq_CBg
Video 2 direct link: http://www.youtube.com/watch?v=3JjE_2o_ov4