It seems related to the rule for *:focus on line 36 of style.css
Focus is usually used to provide indication of a selected element, commonly anchors so that those who are tabbing through links rather than clicking them can see the link they are currently focused upon. The outline property, which is the usual focus default for anchors, has been set to none, but due to the asterisk in the selector the declarations - including float, width, height and clear - are being applied to any element that has focus.
It appears that browsers cope with this in different ways. IE8/9 are the least tolerant, with elements out of place on page load and jumping all over the place when clicked.
Remove the asterisk.
Remove all declarations other than outline:none;
Do some research into :focus to find suitable alternatives to outline:none that you can apply selectively to anchor elements. It's best to provide some visible indication of links for those who navigate via keyboard or assistive technology.