After JN had to check out the current source and build to get around a recent bug, I took the opportunity to go through the same process, create an eXist war file:

• mkdir exist_trunk
• cd exist_trunk
• svn co http://exist.svn.sourceforge.net/svnroot/exist/trunk/eXist .
• ./build.sh clean
• ./build.sh download-additional-jars
• cd extensions
• cp build.properties local.build.properties
• [Edit local.build.properties to turn on FOP.]
• cd ../
• ./build.sh
• ./build.sh -f build/scripts/jarsigner.xml
• ./build.sh dist-war
• mkdir [tomcat]/webapps/exist
• cp dist/exist-1.5....war [tomcat]/webapps/exist
• jar xfv [tomcat]/webapps/exist/exist-1.5...war

Then I started Tomcat 6.0.26, but eXist failed to start. So I installed the latest Tomcat (7.0.12). It took me a while to get this going, but I eventually figured out that all the .sh and all the .jar files in the bin directory need to be executable. I used my usual utf8-startup.sh file to start it up, and exist came up working fine. So the latest eXist seems to prefer the latest Tomcat.