The error in question is:
Could not open Hibernate Session for transaction; nested exception is java.lang.UnsupportedOperationException: Not supported by BasicDataSource

Stack Trace:

Caused by: java.lang.UnsupportedOperationException: Not supported by BasicDataSource
at org.apache.tomcat.dbcp.dbcp.BasicDataSource.getConnection(BasicDataSource.java:899)
at net.sf.hibernate.connection.DatasourceConnectionProvider.getConnection(DatasourceConnectionProvider.java:56)
at net.sf.hibernate.impl.BatcherImpl.openConnection(BatcherImpl.java:292)

The probable cause is that in Tomcat 6, the supplied DBCP database pool does not support the passing of username/password credentials from the application - you have to configure them in the datasource config itself. This issue will only affect people who are using a Tomcat-configured datasource to connect to their database. People using Confluence's internal connection pooling will be fine.

I'm investigating possible workarounds now.