Update - February 26, 2013
The update was not in iOS 6.1.2, but will likely be included in the next update, 6.1.3.
Update - February 15, 2013
Apple has acknowledged this issue and rumor has it they will be including a fix for this and battery-draining issues in the iOS 6.1.2 update, which should be released next week. This bug serves as a good reminder: As there have been lock screen bypass flaws in many iOS versions, it's a good idea to remote-wipe phones that have been lost or stolen.
Much like what happened in iOS 4.1 in 2010, it's been discovered that iOS 6.1 has a lockscreen bypass bug that will allow someone with physical access to your phone the ability to see all sorts of things (especially contacts and photos), even if it's locked. There have been a lot of people hyperventilating about this problem being totally catastrophic, and while it's certainly not a positive, I don't think this is a harbinger of the End of Days or anything.
Considering how many people don't bother to lock their phone to begin with, that significantly shrinks the target market of people who would be irritated by this problem. Add to that the need to have physical access and this becomes a significantly smaller problem. If you manage not to hand your phone to someone you don't want seeing your phone's data (or manage not to have it stolen or lost), you'll be unperturbed by this issue. Just be aware that this is issue exists, and that there will undoubtedly be an update to fix this before long.