Yup. I'm new to the S6 and to Android, and I have to say that the whole notification maze has been a nightmare for me. To your issue, the only way I can dismiss a notification from the notification tray at the top-left of the screen is if I swipe the notification away from the pulldown notification shade (and that is from the home screen, after the phone has been unlocked). If all I do is unlock the phone, and read the email (or text), the badge icon on the app disappears but the icon in the notification tray remains.
So there are 3 areas of notifications -- the notification tray at the top, the swipe notifications from the pulldown notification shade, and the badge icons on the apps themselves. You would think that by reading the email or text to which the notification applies, all would disappear...but that is not how things are working. Each email gets opened...then I still have to pulldown the notification shade and swipe away the notification to dismiss the icon up top. It's absurd.
My situation became infinitely more complicated as I came from the blackberry and wanted a functioning LED notifier. Downloaded Light Manager Pro, an app which addresses a bug in the LED light for Samsung devices running 5.1.1 (tried Lightflow but the existing bug causes it to have certain limitations that Light Manager Pro seems to avoid). Add to the mix things called "persistent icons" and it just gets absolutely hairy. I receive "sent email" notifications for every email I send...which in turn have to be dismissed by swiping away the notifiers.
I spend more time dismissing notifications in order to actually receive the few notifications I want...it's driving me nuts. I can't stand the caged-in feeling of Apple, but I don't see how anyone can argue with the fact that their notification system is incredibly simpler and more stable than Androids....at least with what I'm seeing.
Sorry for the rant...