The log message that appears when a notification is not serializable should be at a severity level that causes it to appear by default. This will save a great deal of debugging time for certain mysterious problems. One particular example is if you set the source of a notification to an MBean object rather than an ObjectName and, for whatever reason, the MBean server does not make the replacement.

In some circumstances this will lead to log storms, but this is pretty much always going to be something that you would prefer to hear too much about than not enough.