Improvements to Javascript to ensure cross-browser compatability (Prestashop and osCommerce sites)

I have 3 x Prestashop 1.4 sites and 1 x osCommerce 2.2 site. I need to be certain that the Javascript deployed on each of these sites (principally in the checkout process) is compatible with all versions of IE, Firefox, Chrome, Opera, and Safari. So this is a "tweak and tune" job for a Javascript expert rather than a complete rewriting of code. Previous experience with Prestashop and osCommerce would be good. The need for this work has come to light because IE9 just simply doesn't run the sites as they should be, and effectively prevents customers from completing a purchase.