Symptoms
Customers receive an "Input string was not in a correct format" error when clicking "Continue Checkout" on the shopping cart page (attempting to load checkoutshipping.aspx).
If the store is using the Minicart.UseAjaxAddToCart then this issue may actually throw an error across the whole storefront, not just the shopping cart pages.
Cause
This can be caused by having a blank or incorrect value (text instead of numeric ID) for ShippingMethodIDIfFreeShippingIsOn AppConfig if the order qualifies for free shipping, or if the AJAX MiniCart is used.