You need to delete the lastLogin node of the corresponding XMLCheckpoint element and enable the "Compare in subtree mode" option for the element. Please see the "XMLCheckpoint Element Editor" article for details.
Unfortunately, there is no way to ignore a certain INPUT tag in the Web Comparison checkpoint. However, you can use the XML checkpoint instead of the Web Comparison checkpoint to accomplish your task.
The error occurs because the XML checkpoint's component cannot download your page from the encrypted web site. I suggest that you save the page's source to a local file and check it using the XML checkpoint in your test.
BTW, you can create your custom checkpoint that perfoms necessary checks on your pages using TestComplete's Script Extensions feature. Please see the "Script Extensions" article on our Support Portal.