The Realm implementations did not process the supplied password if the supplied user name did not exist. This made a timing attack possible to determine valid user names. Note that the default configuration includes the LockOutRealm which makes exploitation of this vulnerability harder (CVE-2016-0762).
A malicious web application was able to bypass a configured SecurityManager via a Tomcat utility method that was accessible to web applications (CVE-2016-5018).
It was discovered that the Tomcat packages installed configuration file /usr/lib/tmpfiles.d/tomcat.conf writeable to the tomcat group. A member of the group or a malicious web application deployed on Tomcat could use this flaw to escalate their privileges (CVE-2016-5425).
It was discovered that the Tomcat packages installed certain configuration files read by the Tomcat initialization script as writeable to the tomcat group. A member of the group or a malicious web application deployed on Tomcat could use this flaw to escalate their privileges (CVE-2016-6325).
When a SecurityManager is configured, a web application's ability to read system properties should be controlled by the SecurityManager. Tomcat's system property replacement feature for configuration files could be used by a malicious web application to bypass the SecurityManager and read system properties that should not be visible (CVE-2016-6794).
A malicious web application was able to bypass a configured SecurityManager via manipulation of the configuration parameters for the JSP Servlet (CVE-2016-6796).
The ResourceLinkFactory did not limit web application access to global JNDI resources to those resources explicitly linked to the web application. Therefore, it was possible for a web application to access any global JNDI resource whether an explicit ResourceLink had been configured or not (CVE-2016-6797).