How to find the offending insertion from a BatchUpdateException?

From the Java API documentation of BatchUpdateException:

After a command in a batch update fails to execute properly and a BatchUpdateException is thrown, the driver may or may not continue to process the remaining commands in the batch. If the driver continues processing after a failure, the array returned by the method BatchUpdateException.getUpdateCounts will have an element for every command in the batch rather than only elements for the commands that executed successfully before the error. In the case where the driver continues processing commands, the array element for any command that failed is Statement.EXECUTE_FAILED.

Now, I'm unsure about the behavior of the Oracle JDBC driver that you are using, but it is apparent that either of the techniques mentioned should work - if there are N elements in the array returned by the call to BatchUpdateException.getUpdateCounts, then N elements in the batch have been processed. Or, if the array returned has the same size as the number of batched statements, then all the array elements whose value is Statement.EXECUTE_FAILED would have failed execution in the batch.