Is it possible to determine whether an email I received was sent over TLS?

Solution 1:

The mention of TLS in the line

Received: from [...] (mail180-123.mandrillapp.com. [...])
          by mx.google.com with ESMTPS [...]
          (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128);

makes it very clear that the connection from Mandrill to GMail was indeed TLS-protected.

The same is true for the very fact that ESMTPS (secure ESMTP) was listed as transport, see RFC 3848.