Magento – CE1.9.1 Please make sure your password match issue during User registration

I found the answer. var con and var pass are the names of inputs so I made new two validators and code looks like this

['validate-password-checkout-register', 'Please enter 6 or more characters. Leading or trailing spaces will be ignored.', function(v) {
    var pass=v.strip(); /*strip leading and trailing spaces*/
    return !(pass.length>0 && pass.length < 6);
}],

And

['validate-cpassword-checkout-register', 'Please make sure your passwords match.', function(v) {
            var conf = $('billing[confirm_password]') ? $('billing[confirm_password]') : $$('.validate-cpassword-checkout-register')[0];
            var pass = false;
            if ($('billing[customer_password]')) {
                pass = $('billing[customer_password]');
            }
            var passwordElements = $$('.validate-password-checkout-register'); //used my validator for password
            for (var i = 0; i < passwordElements.size(); i++) {
                var passwordElement = passwordElements[i];
                if (passwordElement.up('form').id == conf.up('form').id) {
                    pass = passwordElement;
                }
            }
            if ($$('.validate-admin-password').size()) {
                pass = $$('.validate-admin-password')[0];
            }
            return (pass.value == conf.value);
        }],

And I also add class validate-password-checkout-register to password input and validate-cpassword-checkout-register to confirming password input.

Check register.phtml name for Confirmation Password should be confirmation.
Because setConfirmation method is used in customer AccountController in various places to set the confirmation value.
If there is some mismatch try changing setConfirmation to setPasswordConfirmation() in AccountController.