In most Windows applications, you can use F4 to expand a currently focused dropdown. How do I do that in IE? F4 focuses on the address bar.
ALT + (down arrow) also works across all Windows applications. (down arrow) on its own cycles the currently-focused drop down through each item. ALT+(down arrow) causes the entire drop down to, well, drop down. I just tried this on the Hotmail sign-up page and it worked there to cause the Date Selection drop down menus to expand.