There is and there isn't.
When you play a media file in the SpeedGrader it is embedded in the page using a VIDEO tag without disabling download. This means that videos and audio can be downloaded by right-clicking on the player (while it's playing). On the menu, you'll have an option to "Save video as..." that will allow you to download the media file to your computer. Note: Don't let the name of the option fool you, it will allow you to save audio files as audio files, it's just the way in which it was embedded that causes the labeling.
I've only confirmed this works with MP4 (video) and MP3 (audio) uploads, but it does work in IE11, Chrome, and Firefox. For some reason, the Record Media option refuses to work on my computer in any browser. :S
If anyone could test the record media options, that'd be great. I would assume, though, that it'd have the same functionality.
If you're looking to do a bulk download, that would require use of the API to retrieve multiple submissions, then scripting to archive them together, and finally initialize the download. It's doable, but it's a bit heavy on the client browser to implement. I'd highly recommend sticking to individual downloads.
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