It was, in-fact, the way that Blogger had created some of its XHTML code. Disabling an option inside the Blogger configuration seemed to fix this problem.

UPDATED:
In order for Blogger to get rid of the invalid <div style="clear: both;" /> you need to go to: Settings > Formatting > Enable float alignment and set it to "NO." The reason this is coming up invalid, in my situation, is because the posts are entered inside a paragraph tag, where XHTML does not allow a div clear element, apparently. I suppose if I had images inside (which is what this option is there to handle), it wouldn't have any problems, though I can not be sure.