How do I hide Quicktime Player's controls when the video is paused?

In case no solution for Quicktime is found, here is a solution for movie snapshots using the VLC Media Player.

In the preferences disable Add controls to the video window and click Save. Now you can take a snapshot as explained in my other answer.

You can take a screenshot without the controls:

1. Move your mouse cursor out of the quicktime window. (The media controls disappear.)
2. Press ⌘+⇧+4 then space
3. Move your mouse cursor back into the quicktime window. (The media controls stay hidden)
4. Click your mouse to take a picture.

More tips on how to take screenshots in MacOSX can be found here.

I had a problem with Quicktime Player hiding the controls without returning them at all during playback. On my own I discovered it was due to Quicktime's settings left over from an upgrade.

This is what I did to reset Quicktime Player's Settings to factory defaults:

defaults delete com.apple.QuickTimePlayerX

This helped me, and I hope it helps someone else.