I am trying put place a Facebook Like-Box on a page on my site, and then style it via my own CSS (chiefly to increase the height awarded to div#stream_content. (The idea is to
I went this route too. Although you are using FBML, the actual embedded code ends up being an iframe anyway. (you can see it in the DOM with an HTML inspector after it loads). About the only thing I was able to do was put it in a div with a colored background, since the iframe is transparent, and a border.
You are probably getting errors since the javascript on the Facebook server is trying to access the CSS on your server. I didn't think you could do this.
EDIT:
In the StackOverflow link you provided, the posted answers clearly state that using your own CSS only works with a "Fan" box, not with a "Like" box.