It's odd that you are instructed to enter the setting manually. The next time you see that, could you possibly capture a screenshot of it? This article has suggestions on how to do that: How do I create a screenshot of my problem? Please cut out or blur any sensitive information in the image before attaching it to a reply.

I don't know whether it will work, but MP4 video may be sent with a content type of video/mpeg so you could try setting that to the desired application.

And/or if this is a site that doesn't require a login, do you want to give a link to the page where the downloads have this behavior?

I just refreshed my FF.. now I have an mp4 setting in applications. I could have sworn that wasn't there before! I have it set to automatically open such content with Windows Media Player, and FF does show this as the default method of handling mp4's.

Repeat downloads from this site do not elicit the dialog box. However, if I close and reopen the browser, I still get the dialog box suggesting that I can set the preference in FF, rather than it being automatically handled.

http://goes.gsfc.nasa.gov/

Setting unchanged when reopening browser.