Got it figured out. After looking at this example web.xml file for the sitemesh plugin, I ended up with a working web.xml file. Here's what it looks like for anyone else having this problem:
<display-name>Test</display-name>
<context-param>
<param-name>contextConfigLocation</param-name>
<param-value>classpath*:applicationContext*.xml</param-value>
</context-param>
<!-- Filters -->
<filter>
<filter-name>struts-prepare</filter-name>
<filter-class>org.apache.struts2.dispatcher.ng.filter.StrutsPrepareFilter</filter-class>
</filter>
<filter>
<filter-name>sitemesh</filter-name>
<filter-class>com.opensymphony.module.sitemesh.filter.PageFilter</filter-class>
</filter>
<filter>
<filter-name>struts-execute</filter-name>
<filter-class>org.apache.struts2.dispatcher.ng.filter.StrutsExecuteFilter</filter-class>
</filter>
<filter>
<filter-name>struts2</filter-name>
<filter-class>org.apache.struts2.dispatcher.ng.filter.StrutsPrepareAndExecuteFilter</filter-class>
</filter>
<filter-mapping>
<filter-name>struts-prepare</filter-name>
<url-pattern>/*</url-pattern>
</filter-mapping>
<filter-mapping>
<filter-name>sitemesh</filter-name>
<url-pattern>/*</url-pattern>
</filter-mapping>
<filter-mapping>
<filter-name>struts2</filter-name>
<url-pattern>/*</url-pattern>
</filter-mapping>
<filter-mapping>
<filter-name>struts-execute</filter-name>
<url-pattern>/*</url-pattern>
</filter-mapping>
<!-- Servlets -->
<servlet>
<servlet-name>dwr</servlet-name>
<servlet-class>uk.ltd.getahead.dwr.DWRServlet</servlet-class>
<init-param>
<param-name>debug</param-name>
<param-value>true</param-value>
</init-param>
</servlet>
<servlet>
<servlet-name>jspSupportServlet</servlet-name>
<servlet-class>org.apache.struts2.views.JspSupportServlet</servlet-class>
<load-on-startup>5</load-on-startup>
</servlet>
<servlet-mapping>
<servlet-name>dwr</servlet-name>
<url-pattern>/dwr/*</url-pattern>
</servlet-mapping>
<!-- Listeners -->
<listener>
<listener-class>org.springframework.web.context.ContextLoaderListener</listener-class>
</listener>
<!-- Welcome file lists -->
<welcome-file-list>
<welcome-file>index.jsp</welcome-file>
<welcome-file>default.jsp</welcome-file>
<welcome-file>index.html</welcome-file>
</welcome-file-list>
</web-app>
Now that warning is gone.