After upgrading to iOS7, hold the Home and Power buttons for 5 seconds to force the phone off then press the Power button to turn it back on. Here is a before and after of the settings screen for Notifications showing what was missing (I wasn't seeing Weather or Calendar in the Notification screen itself either), Lord knows what else wasn't working right until doing the reboot:
(Note the "Today View" section)

(Note the "Today View" section)

