I'm building a site and need separate sheets for different sections rather than one huge one.
I'm thinking of taking all the consistant structural parts into one base.css and then adding the rest in a second sheet for each section, ie: product.css info.css sale.css

This seems like it would be better since if I redefine a style on different sheets, I'd have to change all of them all to make a global change.  If I do separate sheets, I can change the headers and footers overall in one sheet.

Is there any downside to using multiple style sheets in the site?

I searched and haven't found any negatives for it.

P

You're specifically looking for negatives, so here's a very small one.  In order to have a fast site most web masters reduce the number of http requests made to their server.  Two style sheets = 2 requests.

It's a very small point.

That being said, I use 2 style sheets.  One for layout and another for fonts/images/etc.  I use a template system that manages multiple sites, so this makes it easy to change the look of one site without messing up the layout.

Actually, with one of the css sheets being default for all pages, it'll only have to be loaded once for the whole site.  That means as you move from page to page, your browser will only have to load the page specific sheet which will be much smaller.  This is what I do on my sites.