I've put some code about line caps and joins in Processing & OpenGL up on Processing Hacks in case it's something that bothers you too. I've not tested it extensively so I'd welcome bug fixes and suggestions there, or in the comments here. One thing I'm interested in doing next is extending (or reimplementing) BasicStroke to generate shapes for thick polylines with varying line thickness. If that's something you've done before, please let me know.
I'm using Java's BasicStroke to generate the path outlines, and GLU's tesselators to generate a mesh that will fill correctly in OpenGL. I "borrowed" the code for the latter from Ben Fry's PGraphicsOpenGL font rendering â€“ thanks Ben!