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If you have Quicktime Pro, you can select the down arrow on the right of the player to save the file you are playing.

If you don't, there's at least a workaround: In the preferences, go to "Plugins" and disable the Quicktime plugins. Note that you have to disable "QuickTime Plugin.plugin" as well as "QuickTime Plugin.webplugin" if you have both. Restart OmniWeb, and the file will download to your desktop (or whatever you have defined as your download dir).