Can I tell itunes to download a specific podcast on Saturdays only?
You can use the following AppleScript:

tell application "iTunes"
    set aList to every track of playlist "Podcasts" whose album is "podcast_name"
    repeat with aTrack in aList
        set aDate to release date of aTrack
        set aWeekday to weekday of aDate as string
        if aWeekday is equal to "Saturday" then
            updatePodcast aTrack
        end if
    end repeat
end tell


I would save this AppleScript as application and execute it whenever you want:


Open the application "AppleScript Editor" in the Utility folder.
Paste the code above.
Set "podcast_name" to the name of the podcast
you want to update.
Save the Apple Script as application.


To schedule this AppleScript, you can get hints at the tutorial I found.