Admin header duplicates tabs and links in theme

The admin header does quite some duplication: the tabs sometimes appear in the node form area, sometimes in the D7UX tabs area. This is how it looks when you edit a node:

And it looks like this when you add a node:

The meta information tab is not always in the same place.
While it might make sense to distribute the tabs between "the node form" (first screenshot) and "the tab area" (Screenshot 2) this needs a clear concept.

I presume it is not easy to hijack tabs from the theme and display them in the header. Even more so as this has to make assumptions about the main theme of the site: If someone does not implement tabs in a stardard way, the admin header is screwed and can't be blamed.

Other links affected: The "add content" link which is normally in what we sometimes call "User Menu" and is found in the Video as "Manage".
If the "add" link is in the header, it should not be duplicated in the "theme area".

I guess there is more trouble like this that I have not found yet. How about using this issue for collecting these and splitting up into seperate issues if needed.