The cart objects are appearing to slide out to the right, because the closing tag of the productCart (class) div is missing or misplaced. This means that each new productCart (class) div added to the page when an 'add to basket' occurs is placed inside (or appended to) the previous one. They would nest recursively, hence the shifting to the right.
Adding a closing </div> tag in Firebug put it right.
In my cart.php file, the closing div comes immediately before the lines:
Lines 376-381 (in mine)