Hi there,
I just checked your css and the issue is because of a rule you added:
ul li a {
font-size: 1.2em;
line-height: 1.8em;
}
This code increase the size of your font and the calculated size of the sliding module cannot adapt to this... So you just have to override or delete this css and the module will works well
.
To edit the css you have to go in System>Configuration>Display and edit the front end css file.
About the menu, I meant the bottom left option called "menu", you have to select there your category listing
.
EDIT: try with line-height: 1em; and no font-size and you'll see it's working