Can you use copyrighted material, such as copyrighted songs or pictures, in your #SciFund video? The question of what is allowable use of copyrighted material is quite complex legally. Accordingly, it is left to the discretion of individual SciFunders whether they use copyrighted material in their campaign or not.
One way to be sure that you are in the clear is to only use materials that you created yourself, got permission to use from the owner, or is Creative Commons licensed. To focus on the last one, there is a giant amount of Creative Commons content out there. You are free and clear to download all of it and to use it in your own work.
Great clearinghouse sites that I regularly use to find Creative Commons-licensed stuff:
Music: ccMixter (awesome search feature here)
Sound effects: Freesound
Images: Wikimedia Commons (there is also audio and video here, but images are the star of the show here) http://bit.ly/IaNS8Q
Images: Creative Commons on Flickr
There is a bit of a caveat that I should mention, which is that there are different kinds of Creative Commons licenses. Each license type varies a bit in terms of what it allows you to do. In general though, the whole point of a Creative Commons license is to encourage the use and modification of the content that is under that license.