Unfortunately, you can't disable the comment box from popping up. Facebook wants that to show as it allows the user to provide extra social context as to why they clicked the Like button. It's not required, but if a comment is used, it greatly increases the chances of that Like button being included in their news feed.
I'm assuming that area that the Like button is in is an iFrame, and that's why it's causing the scroll bars to appear. Is there any way to move the Like button out of that, to under the picture, for example?
There's lots of ways we can help style things so that the comment popup works, but it's just not an option to hide it altogether.
I hope that helps explain a little,
Alex