When my viewport size reaches about 500 pixels I want to rearrange the layout -- e.g. move the nav menu down, make the hero unit span more columns, etc. I can't figure out how to do that. Whenever I make that kind of change at the breakpoint it is reflected up into the rest of the project.

Assuming that you start with the wide viewport.
Remember to actually set the breakpoint where you want to start rearranging it.
Then make sure that the slider hasn't moved away from the breakpoint, there has to be a black dot in the middle of the breakpoint.
Then you can start editing your layout.

OK, here's how I tried to do it:
I move the slider to 500 px
I click the '+' sign to set the breakpoint (the black dot is showing)
I click on the nav row and use the "move" arrow to move it down
At that point the row is moved in the entire project (so it seems)
Is there a different method I should use or a step I'm missing?

Media queries have been designed to apply different styles (CSS) at certain widths. Places where that happens are called breakpoints. The specification does not allow for moving or replacing content (HTML), so moving a row down will apply to any width.

In short, at any breakpoint you can change 1. the widths of columns by changing the span-width on the layout pane, and 2. the style settings on the Design Pane (font size, margins, display etc).

Hope this helps!

Thanks.
I've done this sort of layout manipulation using CSS only and assumed RSD would use that method. Since I'm just learning RSD, I haven't discovered yet if there is a way to use classes, ids and other selectors in this way in RSD. Any tips?

Yes, Bob said exactly what I wanted to say.
A workaround could be to make two menus, one for wide screen and another for viewports below 500px, and then position them where you want them to appear. Then use display rules to show only one of them.

Something to remember:

If you make changes to a type or class at a breakpoint on a particular page, elements with the same type or class on other pages will be affected at the same breakpoint on their pages.

If you have an element that appears on several pages, but you only want to affect it on one particular page, give the element to be changed an ID and make changes to the ID. Make sure that you DO NOT give the same elements on the other pages the same ID.