If it's the posts, I don't get why the sidebar is affected...
The sidebar code typically comes AFTER all your post content, just that the layout instructions tell it to live side-by-side with the content.
That's why if you have broken content, the sidebar will be affected (even seemingly above the point where your content is broken)
And I know the validator sees the same page I'm seeing, but I'm not sure exactly where that is. Do you know what I mean?
Yes, I know what you mean. The page you see when you visit your site in a browser is assembled with a rather complex series of actions performed by wordpress.
When you add content to your site, you're adding it to a database, and to display that content the wordpress software then extracts it from the database, performs it's magic, and stuffs it into whatever theme you happen to be using. All this happens behind the scenes to generate the 'page' you view when you hit your website.
The validator sees only the result of this process, not any "files" you may or may not have uploaded.
WordPress itself works, so you don't need to worry about that. The only files you should be concerned with are those comprising the theme you're using - and if the same issue happens when you change themes then you can likely ignore those too.
The rest is all in your posts, and those don't exist anywhere outside the database.
By the way, while a five year old may look like they know more about your VCR than you do, they really have no idea how it works... and trying to explain it to a five year old would involve words like 'magic' :)