iOS 7.0.6 and 6.1.6 for iPhone and iPad released, go get your bug fixes! [Update: Apple TV too!]
"This security update provides a fix for SSL connection verification."
Update 1: Apple has posted the security update contents.
We'd hoped Apple would address the deeper issues, including the frequent re-springs suffered by many users on iOS 7, but that still seems to be waiting on the too-long-in-coming iOS 7.1 update on track for March. If you download and install the update, let us know how it works for you, and if you see any other changes, tell us all about them.
Update 2: Apple has released a matching update for the Apple TV, version 6.0.2.