I've narrowed the problem down to the theme. When I switch themes, everything's fine, but this theme is working well for me, apart from this problem. Right now, spoilers just show up as:
The text within the spoiler tags
I am using compatibility mode and I also used the WYSIWYG button to add the shortcode, so I know I didn't mistype something. I'm very comfortable editing theme files - I just need to know where the problem might lie. Thanks!