After I spin up Accumulo in a Docker container, well-known ports (like 2181 for Zookeeper) are not well-known any more. The internal private port (i.e., 2181) is exposed as a different public port (i.e., 49143). Java program trying to connect to Accumulo must automatically find the public port numbers.
The java code below finds the public port for Zookeeper for a Docker container named "walt". I don't know why the slash is needed in the image name.

int wantedPublicPort = -1;

        String wantedContainerName = "/walt";
        int wantedPrivatePort = 2181;

        String dockerURL = "http://127.0.0.1:4243";
        String dockerUser = "medined";
        String dockerPassword = "XXXXX";
        String dockerEmail = "david.medinets@gmail.com";
        DockerClient docker = new DockerClient(dockerURL);
        docker.setCredentials(dockerUser, dockerPassword, dockerEmail);

        List<Container> containers = docker.listContainersCmd().exec();
        for (Container container : containers) {
            String[] names = container.getNames();
            for (String name : container.getNames()) {
                if (name.equals(wantedContainerName)) {
                    for (Container.Port port : container.getPorts()) {
                        if (port.getPrivatePort() == wantedPrivatePort) {
                            wantedPublicPort = port.getPublicPort();
                        }
                    }
                }
            }
        }

        System.out.println("Zookeeper Port: " + wantedPublicPort);

In order to use the DockerClient object, I added the following to my pom.xml:

gt;
    gt;com.github.docker-javagt;
    gt;docker-javagt;
    gt;0.9.0gt;
  gt;

As a simple lay programmer, I sometimes have trouble figuring out where log files are stored on unix systems. Sometimes logs are within application directories. Other times they are in /var/log. With Docker containers, this uncertainty is eliminated. How? By the 'docker diff' command. I will show why. When connecting to a Docker-based system, you can see the running containers:

$ docker ps
CONTAINER ID        IMAGE                     COMMAND             CREATED             STATUS              PORTS                                                                                                                                                                                                                                                                                                                                    NAMES
90a9f7122c02        medined/accumulo:latest   /run.sh walt        9 hours ago         Up 9 hours          0.0.0.0:49153->50070/tcp, 0.0.0.0:49154->50090/tcp, 0.0.0.0:49155->50095/tcp, 0.0.0.0:49156->8025/tcp, 0.0.0.0:49157->8030/tcp, 0.0.0.0:49158->8088/tcp, 0.0.0.0:49159->10020/tcp, 0.0.0.0:49160->19888/tcp, 0.0.0.0:49161->2181/tcp, 0.0.0.0:49162->22/tcp, 0.0.0.0:49163->8020/tcp, 0.0.0.0:49164->8050/tcp, 0.0.0.0:49165->8141/tcp   walt

Then you can list changed files within the container using the image id or name.

$ docker diff walt
...
D /data1/hdfs/dn/current/BP-1274135865-172.17.0.10-1404767453280/current/finalized/blk_1073741825_1001.meta
...
A /var/log/supervisor/accumulo-gc-stderr---supervisor-5H7Rr7.log
A /var/log/supervisor/accumulo-gc-stdout---supervisor-LK8wDU.log
...
A /var/log/supervisor/namenode-stdout---supervisor-mciN4u.log
A /var/log/supervisor/secondarynamenode-stderr---supervisor-EaluLZ.log
A /var/log/supervisor/secondarynamenode-stdout---supervisor-Ap4Fri.log
C /var/log/supervisor/supervisord.log
A /var/log/supervisor/zookeeper-stderr---supervisor-CCwUGw.log
A /var/log/supervisor/zookeeper-stdout---supervisor-lDiuIF.log
C /var/run
C /var/run/sshd.pid
C /var/run/supervisord.pid

Armed with this list you can confidently either look in /var/lib/docker or use the nsenter command to join the namespace of the container to read interesting files.