I ended up fixing it by applying a position: relative; and z-index: 100; to each <p> tag. Nothing below 100 would display the text.
It turns out its a variant of the Internet Explorer 6 peekaboo bug. One of the guys over at Stack Overflow pointed me to a blog post on small-software-utilities.com where they listed finding a similar bug in Internet Explorer 7. Interestingly, their fix didn’t do it for me. I had to apply the z-index as well as the relative positioning before it was fixed. It would be nice if Internet Explorer could at least be consistent in it’s bugs!
Thanks to everyone that helped out!