Spurred on by a report of some fun stuff at the city council meeting last week (turned out to be a yawner, but that's for later), I went to the city website looking to download the video. There's actually a feed for a podcast, but content hasn't been put on that particular feed since 2007.
There's also a roundabout way to download the videos via the stream their published on.
But, the most direct way is to poke around for an RSS feed that the city's contractor publishes on the video front page. There is no direct link to it, but if you're using Firefox, you click on the radio logo in the URL bar, and its the first one in the list that pops down.
Here is the direct link.
From that feed, you should be able to find a link to a .wmv file that is published in no other place on the city's or their video hosting contractor's website. The files are usually more than 200MB, but if that doesn't bother you, you can download a useable file to edit and repost as you see fit. I mean, if you live in Olympia, you're paying for it, so you might as well use it.