New apps launched today - December 7, 2010. With the new free OverDrive Media Console app you can download both EPUB eBooks and MP3 audio eBooks directly to your iPhone or Android phone.
Update: if you've downloaded the previous version of Overdrive's app, and are having problems with the e-books appearing after you download them, you may need to delete the app and download it fresh. See commenter Mark's thread below.
If you are having trouble, first make sure that you have current software update from Apple.
Then make sure you have the Overdrive app--the recent update of the Overdrive.
Overdrive help menu advises that you "reboot" after you download the app (turn your device off, and then turn it on again)
PC magazine / zdnet are geeked on Bluefire Reader for the iPad, a different app available from the app store, and reviews there are good. Maybe try that. Good luck!
Here's a short preview of the new app. This might help you get started.
Are there plans in the future to add more Epub titles for mobile devices? There has been 1100 available since launch, what are the plans to expand this number? Just wondering since this is considerably less than the library ebook catalog currently available on a MAC/PC.