Hi Barnabee & Warner,
did you use icloud to set up the devices? My iPhone 5s is fine, but my iPad Air continously went on about having to provide the password for my facebook account referring to the email address I have not used in 3 years.
Long story short, my issues were resolved after Jason (thank you again) from the Apple Care Support team told me to wipe the entire device and set it up without relying on icloud.
Takes time but does the job and then I called back to tell them to push this to the tech developers, because this clearly is an issue Apple needs to address. the Twitter integration (I run 4 accounts) is also glitchy and I hope that this clean slate restart/configuration allows me to enjoy the same trouble free experience I was used to from my iPhone 4s and iPad 4 Retina even whilst running iOS 7.0.4
Regards,
Dan