So IE8 comes set up in such a way that breaks Sitecore functionality pretty handily, including:

Smashing pop-up menus and displaying horrible scrollbars on them (like when you're inserting a new page…) AND

Disabling the drop-down menus on the WYSIWYG editor.

Fortunately, the fix is pretty easy:

In IE 8, go to Tools – > Internet Options -> Security –> Trusted Sites –> Custom level. About halfway down the giant list of security settings, you’ll see an option for "Allow script-initialized windows without size or position constraints." Set this to ENABLE.

Choose "OK" to apply the settings changes.

Next, do the exact same thing under Tools – > Internet Options -> Security –> Internet –> Custom level.

Once you've made these changes, be sure to choose "OK" to apply them.

Finally, to ensure the new settings take effect, restart your browser.

These changes should resolve the issues.

Happy Sitecore-ing!