Recently I was part of a group that met twice to discuss redesigning Thurston County's currently horrible website. To put it shortly, the website is a reflection of a lack of technical progress (the pages are still manually built from an html editor) and the disjointed governance of the county.
The website being in the technical backwoods is less troubling to me because the website is actually very informative. The county's technology manager attended our second meeting and said that getting everything possible on the website had been their first concern. To me, that puts them on good footing for where they need to go next.
And, despite the casual framing of the project as "redesigning" the county's website, that is the last thing they need to do. Yes, its ugly right and it should be prettier, but not prettier in terms of a slick design. Drastically simple designs like craigslist.org's or wikipedia's would get the county where they need to go.
So, I wouldn't call it a redesign, but rather a restructuring. The first step should be scrapping their current method of updating the website and implementing a Content Management System. Easier, open source solutions are available, but it sidesteps the concept of a "redesign," which would seem to focus on the aesthetic and drive you toward the usable.
And, just one more thought:
I like RSS feeds a lot. If I could subscribe to a portion or an entire government website, that would be great. I've created some Pag2RSS feeds for some parts of the city of Olympia's website (like city council agendas and planning commission), but an entire government website with RSS tied to it would be great.