B2B operates in two modes for default internal queue communication - AQ and JMS. This is controlled in the Admin/Configuration page "use JMS queues" checkbox.
In AQ, the queue to which the exception message is delivered would be IP_IN_QUEUE
In JMS the queue to which the exception message is delivered would be B2B_IN_QUEUE. Since you speak about reading error message from the JMS queue directly, am thinking this would be the one of interest to you.
In addition to the above we can create custom JMS internal delivery queue and this can be associated to the Exception Queue which can be assigned in the Admin/Configuration page.
With regards to reading the exception msg specific to the trading partner from the JMS Queue directly, this can be done by adding a check on the dequeue process. Each exception message is populated with From_Party and To_Party information. In the outbound delivery case, the exception message should have To_Party set as the partner's name. This can be checked.
Hope that helps.