Although 404 errors are a general 'not found' error, in this particular case one of our clients encountered a 404 specific to an RSS feed that was supposed to be generated by a Podcasting plugin. Although the feed file was in fact generated, WordPress was returning a 404 when services (like iTunes) were attempting to read the feed and add the newly posted podcasts to their listings.
It was discovered that WordPress wouldn't publish any feeds unless its 'blog' / 'posts' feed had something in it first. Therefore the workaround was to publish a single blog post (even if it's not visible on the website itself) to have WordPress generate a blog RSS feed. Once the blog RSS feed was populated, feeds created by plugins began working without a 404 error any longer.