The website collects various test cases for insecure TLS connections, such as expired or incorrect hostnames in certificates. I can get many of them to pass by using explicit settings:

    -tls1 0 -tls1.1 0 -tls1.2 1 -require 1 -cafile -cipher {ECDHE-ECDSA-AES256-GCM-SHA384 ECDHE-ECDSA-AES128-GCM-SHA256 ECDHE-RSA-AES256-GCM-SHA384 ECDHE-RSA-AES128-GCM-SHA256} -autoservername 1

But others seem to be impossible to pass the tests with the current library. I can manually fix the hostname/wildcard matching by using a -command callback (there is another bug covering this), but I cannot either get it to reject a revoked certificate or a SHA-1 intermediate cert. These could be done via the -command callback, but unfortunately the raw certificate field passed to this callback is truncated so cannot be parsed.