One issue that Ive came across with Quicktime (and judging by the number of posts about it that Ive came across on the internet Im not the only one), is the issue where Quicktime stops responding to keyboard commands, for example the spacebar no longer plays or pauses and so on.
It mainly seems to occur if you put a video into fullscreen and then for whatever reason, close fullscreen but still live the window with the video open on the desktop. Afterwards it will not respond to any keyboard commands unless you put it back into fullscreen.
Tabbing between applications until you get back to Quicktime does not resolve the problem, neither does moving it to a different workspace.
Other posts on the internet suggest reinstalling Quicktime by downloading the standalone file from Apple. Although I havent tried this yet, I have found a workaround that seems to fix the issue temporarily.
It appears though, that minimising Quicktime to the dock and then restoring it, is enough to put the focus back on the application.
Update : It seems that my solution may not be as reliable as I first thought, Ive tried it just now and it didnt work... will take another look at it and post anything I find here.