What's galling about the notice that it's "cumbersome" to leave a note about changes is how widespread the practice is at other publications. I used to write for Wired and if there was a minor change, say mispelling someone's name in the story, we'd add a note to the footer highlighting the change. Same with Slate, a well respected news outlet that will add a footer for minor changes. When rewriting the story wholesale it doesn't seem a stretch to leave a footer, or at least a timestamp that highlights when a story is "complete."
Could Wired show a version number with a story? Click it and one could see the various changes publicly published online. Perhaps diffs and comments, like any version control system. It seems one could do much more online than the limited footnote or corrections page we get with print.