Q: My iPhone 4S “remembers” my previous Apple ID (also previously my email address) even though I have adopted a new email address that has been verified by Apple; it is also my new email address. So, when I try to log in to the Apple Store, it displays my old email address thereby resulting in an error message that either the ID or the password is incorrect. Any ideas?

– Ron
A: Unfortunately this is a known problem with iOS when changing your Apple ID. Basically, content that was purchased before you changed your Apple ID remains associated with the name of the old Apple ID. This most commonly becomes an issue when updating apps; since iOS just reads whatever is stored in the actual app header, you end up getting prompted for the name of that prior Apple ID.
You can actually observe this in iTunes; if you select an older purchased item in iTunes and look at its summary page by choosing Get Info from the iTunes File menu, you’ll see that your former Apple ID appears in the “Purchased by” section.
Note that this only applies to the items that are already stored in your library or on your iOS device. Since the purchaser information is added at the time of download, you can actually correct this problem simply by re-downloading the affected content directly from iTunes in the Cloud rather than syncing it on via iTunes on your computer.
While this is relatively straightforward for media content, it’s not really practical to handle for apps on an individual basis, since deleting an app also removes all of the data for that app. In theory, the problem would eventually go away as all of your apps get updated, since the updates will contain the correct purchaser information, but that’s not going to be a practical solution if you have a lot of apps, particularly considering some may never actually receive updates.
The only effective way to really deal with this is to completely restore your iPhone from an iCloud backup. This process basically reinstalls all of your apps and media by downloading them from iCloud along with your data, resulting in the apps carrying the current purchaser information. Our Guide to Transferring your Content to a new iPhone, iPad or iPod touch provides more details on the iCloud restore process. You should be able to fully backup and restore your device via iCloud without losing any data, although it will generally take an hour or two to do this, depending on how much is stored on your device. Note also that this will only restore purchased content, so you will likely still need to sync with iTunes afterward to restore anything else such as music or video content that you’ve imported from other sources.