I'm not sure if you might be misinterpreting the OP, or if I'm missing something. He's not worried about getting notifications on both his iPhone and his computer, but the fact that the notification doesn't disappear on his computer despite having been checked on his phone.
I think you are missing something. The problem is that when you get a notification you get it on all devices, even when you open your notebook. The video clearly shows that. It also shows that when you mark the notification as being seen it will reflect that on the other device. What the video does not show is what happens when you open the notebook after you've marked it as seen. Will it still show in the notifcation centre but as being seen or will it not be shown at all?
The current problem is that you get a notification on all of your devices and you need to mark them as seen on all of them. It currently doesn't even work between Mountain Lion versions. With iOS 6 it will work between iOS 6 and Mountain Lion and hopefully between Mountain Lion and Mountain Lion as well. At least that prevents the problem of needing to mark the notification as seen on all of your Macs and devices. There is simply much more to it than just iOS 6. The video does not show this. It only shows two devices running iOS 6 (at least that is what I assume as it seems more logical to me).
For me, Messages downloads the conversations, but only notifies me about the messages I haven't read yet...
There are quite some people who don't want that. When you mark it as read it should stay away. You handled the conversation already so it should not show up on any other device. Currently it still does that even if you have 2 Macs running Mountain Lion (again, it is more than just the OS, it is the backend (aka the servers) that need to be configured for this as well).
The way it is implemented now means that everything will be stored on Apple's servers which means that privacy is thrown out the window. To me that makes iMessage completely useless. Messages are the only things that should travel via the servers, they should not be stored on them. History is something that should be locally on the computer/device itself unless the user willingly chooses to have it stored on the server. It creates big problems outside the USA because things are stored on servers in the US by an American company which is subject to the law of their home country (USA). That means it does not follow the regulations in countries outside the USA which makes it unsuited for some people. Something to think about and that's the problem. Apple doesn't tell people this, people actively have to look for it. That's not always a lawful thing to do (in some countries you have to inform customers about these things).
