I had wanted to add the name of the view with its display to the body classes (Views apparently provides everything but that combination, and not all browsers we need to support deal with matching on two sibling classes). Looked in Zen for how to do it first though and as a consequence saw a way to add new sub-section body class with the first two parts of each URL.
This goes in your zen subtheme's implementation of preprocess page:
Except where otherwise noted, content on this site is licensed under a Creative Commons Attribution 3.0 Unported License.