As far as I know there are quite a few keyboard shortcuts one can use in picture-in-picture mode. However, they don't always work for me. Most notably, spacebar often toggles the last thing I clicked in picture-in-picture mode. For example, I enter full screen mode and press spacebar to play the video, but instead it exits the full screen. Or I click on one of the "rewind" buttons, after which spacebar adopts the function of that button until I manually click play. For some reason, the arrow keys also don't always work. I suspect it's the problem of the same origin. I also feel the need to say that this behavior is not limited to picture-in-picture. This is similar to what happens in almost all video players online and, possibly, some of the offline ones as well. I have also checked a few forums (VLC development thread and Stack Overflow) and it seems to be a common issue across many video players. Still, if anyone knows any way to deal with this problem in Firefox picture-in-picture as a user, I would greatly appreciate it, as it interferes with multitasking a lot more than on any other players.