So the current JOSM release allows you to load and save *.osn files. There is a daily notes dump available at http://planet.osm.org/notes/

But you can’t filter them to only display those that are open. I wanted to find a solution. First, I thought about writing Python or C# app. Turns out there is much simpler solution: XPath is a syntax for XML element selection. With xml_grep from xml-twig-tools package I can apply it to an XML file like this:

xml_grep –exclude /*/note[@closed_at] planet-notes-latest.osn > open_notes.osn

You can of course extend this expression to filter by geographic area or date.