How can I correct a typo with Apple ID? How can I use iTunes with an email address that isn't actually an email address?
The answer depends. If you are using an apple email (such as me.com, iCLoud.com, mac.com, etc) then that email address is by default an apple id, and I don't know of a way to edit it.

If you are using a 3rd party email address (such as hotmail, gmail, yahoo, your own domain etc) as your appleid, then you should first TURN OFF FindMyIPhone on your device if it is enabled.  (DO NOT change your primary Apple ID with FindMyIPhone enabled, it can be enabled again as soon as you are done with the changes.)

Next navigate to http://appleid.apple.com and choose the "manage" option, then log in.  An "Edit" button will appear next to your primary appleid.  (if the Edit button does not appear then you are using an apple generated email address such as me.com, iCloud.com, mac.com etc.)

Next on your phone go to the settings app, and log out and log back in for iCloud, iTunes and App Store, iMessage, Facetime, Game Center, and update email accounts if needed).

Once everything is working as expected be sure to turn FindMyIPhone back on.  (It is possible to get out of the mess you create attempting to do this with FindMyIPhone turned on--i did it-- but it is much simpler to just turn it off before starting and re-enable it at the end of the process).