I'd like to take advantage of some JDK7 features. What issues might I run into given that I use Apache Tomcat 7.0.x (latest) and Spring 3.1 (latest)?
There were a few compilation gotchas where JDK 6 could infer the generic type properly where JDK 7 could not. This was apparently a bug in JDK 6 as referenced here.
If you are using container-specific resources (e.g., data sources, etc.) be sure to verify these are still operating properly (though this will be immediately obvious on Spring startup if any of these are wired in).
If you are using Spring Security, and you upgrade, you do not need to make any changes per se to get get things running. However, you should take advantage of their less verbose configuration options (especially for REST URL's) that are available in Spring Security 3.1.
Other than that, our upgrade was seamless.