Twisted before 16.3.1 does not attempt to address RFC 3875 section 4.1.18 namespace conflicts and therefore does not protect CGI applications from the presence of untrusted client data in the HTTP_PROXY environment variable, which might allow remote attackers to redirect a CGI application's outbound HTTP traffic to an arbitrary proxy server via a crafted Proxy header in an HTTP request, aka an "httpoxy" issue.
In words.protocols.jabber.xmlstream in Twisted through 19.2.1, XMPP support did not verify certificates when used with TLS, allowing an attacker to MITM connections.
In Twisted before 19.2.1, twisted.web did not validate or sanitize URIs or HTTP methods, allowing an attacker to inject invalid characters such as CRLF.