1. Start playing the movie in Safari.
2. Open the Activity Window in Safari. It's under the Window menu.
3. Find the movie in the Activity window. The Activity window lists a lot of things, like all the graphics on the webpage (and for all open pages.) But I usually find movies because they are the largest--in the MB's not KB's. Also the movies size is usually changing--as long as the movie is downloading.
In the image below, the movie is the file 3rd item from the bottom whose name starts with v6.cache.googlevideo.

4. Select the movie file in the activity window and copy it. This will copy the location of the video.
5. Open a new browser window and paste the movie's location in the address field.

6. Safari starts downloading the video. Download window should automatically open.

7. Wait for the video to finish downloading. Then find the video file. The magnifying glass next to the file in the Download window will take you to it. In OS.10.4 it's probably on the desktop. In OS 10.5, it's probably in the Downloads folder.
8. Rename the file to add the .flv suffix if it doesn't already have the .flv suffix, e.g., get_video.flv. You might as well add a descriptive title too while you are at it.
Now to work with flash video on the Mac, I use the free Perian plug-in. It lets QuickTime recognize the file, so that you can use it in Final Cut Pro or any app that uses QuickTime.
YouTube now has better quality video available on some videos. Check to see if the video you want is in better quality before downloading. If there is higher quality video, then you'll see the link below the movie "watch in high quality."

Click on that link and then follow the instructions above to get a much better looking video from YouTube.
Earlier this summer I posted a link to a post from Final Cut User that recommends transcoding the flash to something that FCP is used to working with, like the DV codec. I haven't had any problems working with Flash video, but it could speed up your workflow if you don't have to render the movies in the timeline.