The add appointment icon is disabled in Calendar
If your iPhone is syncing with iCloud properly your add button will disappear until the system finishes syncing.  If the sync is frozen, you can toggle iCloud Calendars off in Settings>iCloud, restart the iPhone, and then turn Calendars on again to restart the OTA sync.  If there still is no add button sync iPhone with iTunes to restore the calendar app.  On rare occasions you might have to restore the iPhone firmware.