I'll step out of the shadows for a moment to try to help people with the badges issue, which I also experienced for a few days recently.
After clicking on the "new Badge(s) has/have been earned" notification, you'll be linked to your Badges page, where a dialog will appear in the upper left corner, partially hidding your avatar. There will be as new messages on that dialog box as new badges notifications, and the only thing you need to do to stop getting notifications (it worked for me, at least) is clicking on the 'x' for each one of those messages. Simple, but effective.
I don't know if this will solve everyone's problems with badges, but I post it here in case it's useful to someone.
This is EXACTLY what needs to be done - I couldn't remember what it was, that actually cleared that flag! But yes, that notification in the upper left will display each badge that was earned and each one needs to be dismissed. Thank you for this!!!!!!
I have been testing this issue for the past few days to try and figure out any other useful data for others. Like Verter said, closing the dialog box will prevent more notifications from showing up.
Another way of seeing the block that needs to be closed is by pressing "HOME" on the top bar of the site. then you should be able to see something like this:
All you need to do now is click the (Close) button and the box will disappear.
However, something strange did happen to me while testing this out. I got 2 badges on the same day, but after waiting for an extra day and getting the notifications again, I was only prompted with one of these close messages, and I was only awarded one Badge. There seems to be another badge missing.
By my best calculations, the badge missing is this one: