Does version control have a part in the video production workflow?
Version control in the sense of Git isn't very practical in the video world. You would need to make a specific version control tool for every audio and video tool out there as all work with their own project formats.
But being able to read these formats is just one thing, then you also need the render engine of that tool to show diff's.

Though all of these tools work in a non-destructive way unless you pre-render some stuff (compare that to compiling a dll/lib of a piece of your code and work with that from now on), so you ususally can just go back to an old revision by doing ctrl+z or using the history tool in some programs.

Though saving sub versions is usually the way to go. Like stib described in his answer or by doing it manually.

Something I like to do and works well with every software is putting my project files (no source footage) into Dropbox. If you have a somewhat fast upload speed (~1 Mbit/s) and your project file isn't 100MB+, you can upload your project before you save the next time. An average Premiere/AE/FCP project is around 10-20MB so your recently saved files will be uploaded in 1-2 minutes. Even faster if you have more upload bandwidth.

Then if you have to go back you can access Dropbox's history of your files and download or restore to that revision. Dropbox saves file revisions forever* on a paid account (*atleast when they had the pack rat option, now its a year I think) and for 30 days on a free account. I'm sure that there are other cloud hosters that offer similar features.
It's a bit like using a super limited version of git that handles binary files very well and is headache free.
This has the advantage that you don't clutter the folder with tons of files and have a backup at the same time.

Most cloud hosters also offer Team Memberships so you can work with multiple editors. Or you share the project folder with other team members.