Erin Stellato of SQLskills shows how to use Extended Events to monitor for query plans with certain characteristics, such as joins missing predicates, columns missing statistics, and unmatched filtered indexes.
You may have cases where an ancient application is using an old login or the wrong password. SQL Server is great about auditing failed logins and recording that they happened; it is not so great, however, at providing enough information to locate them. Aaron Bertrand offers some help.
Extended Events provide a way of unintrusively monitoring what's going on in a SQL Server instance. Unlike SQL Server Profiler and SQL Trace, it has little performance impact. Now, in SQL Server 2012 SSMS, it is relatively easy to use, as Robert Sheldon shows.