After much hemming and hawing, I was able to get Apache working as a reverse proxy to Tomcat today.
<VirtualHost *:80>
ServerName domain.com
ServerAlias www.domain.com
ProxyPreserveHost on
ProxyPass / http://localhost:8080/path/
ProxyPassReverse / http://domain.com:8080/path/
</VirtualHost>
That’s all you need (though you can add much more). Note the trailing slashes on the proxy paths – without them, you have no dice.