I have a "movies" page on my site where I allow people to download little 10-40 second clips of things I've done.

According to LIEA I put the download up but when a user clicks on it it begins to download but when it's done a message says it "cannot find the source" or something and it won't play.

I find that if I right click / "Save Target As" it downloads just FINE! is there anyway though that I can just make the download happen by just clicking on the link and not having to right click?

Zip up the movie file would be the best way. Settings to play media files depend on the user's computer/browser and could have varied results, zipping it ensures that they can just open the file or save it to disk as they please.