Migration from 1.6.1.24 to 1.7.6.1 and from 1.6.1.24 to a new installation of Prestashop 1.6.1.24 resulted in inability to checkout, either 404 in 1.7.6.1, or just going back to step 1 in Prestashop 1.6.1.24. I am not sure if it is a problem in our old Prestashop, but rewriting the order URL has solved the problem, so be careful and test it before you use it in production.