This is a simple symptom-cause-solution blog entry only. I hope these blogs will help fellow administrators.
On Unix-based systems, log message like:
Failed to listen on port 8081, failure count: 1, failing for 0 seconds, java.net.SocketException: Too many open files
The value of the "Maximum Open Socket" WebLogic setting is set higher than the the Unix limit (obtained by running the "ulimit -a" command).
Either decrease the value of "Maximum Open Socket" (located on the managed server's Tuning tab) to be less than the Unix limit, or increase the Unix limit. Investigate why there are so many requests being made.
Although this particular issue doesn't seem to be documented, you can see many other SocketException scenarios at http://www.insideexceptions.com/en/jdk-1-5-0/java-net-SocketException.html. It's a very helpful resource.