Sometimes demos will not run on the desired platforms so why not make recordings of your own demos? It might be a cool idea to embed a youtube video of your demo in your contest entry to ensure everyone can atleast see it. I know that those darn lossy video formats will never be the same as they real thing but it is atleast an option when trying to show a demo that will not run.
Basically you should first set up a youtube account. Once that is done and you have confirmed your account via an email link you are ready to begin.
I like to use the program Hypercam
http://www.hyperionics.com/hc/.
I've found it MUCH better than Fraps for making smaller files. I've just started playing around with making vids. The only downside is that the free version will put some text in the upper corner. I'm not saying that you should not submit a demo if you are in a contest you MUST submit a demo. This is just for that chance one or two people who cannot run the production.
Nothing is mandatory of course. This is just a thought.