Overdrive has posted this information regarding their app which is used to download e-books:
"When an existing OverDrive Media Console (OMC) user upgrades to iOS 7, the app will fail when trying to open a DRM-protected eBook. New or first time users of OMC are unaffected by this issue.
"We are resolving the issue but in the meantime, here are immediate remedies for users:
"Audiobook users won't notice that anything is different unless they attempt to download parts of audiobooks they already downloaded to OMC before upgrading to iOS 7. A user will receive an error message informing them to download the title again."