There are a number of problems which could occur when updating the iPhone, iPad or iPod Touch to iOS 7. First, and foremost, make sure back up all iOS data on your iPhone via iTunes or iCloud before proceeding with updating. This will save you a lot of trouble should the iOS 7 update fail.
Be sure to check the following article which will help you resolve some of the most common issues occurring during update to iOS 7: http://goo.gl/axuVqT.
When upgrading, make sure to update iOS via using OTA (over-the-air) update rather than using iTunes. OTA update brings increased reliability of the iOS upgrade process. If you choose to upgrade via iTunes, you might encounter error messages during or after the update.
Here’s a list with the most common problems during iOS 7 update:
iTunes returns an error message during iOS 7 update
iPhone in Recover Mode after upgrading iOS
iPhone data restore incomplete after firmware update