What is the recommended way to present dumps that are auto-generated due to any errors?
Would that just expected to show up as a LogService Entry, and would the expectation be that a client parse through Entries for ones that have "DiagnosticDataType" and figure out that it has to be fetched via AdditionalDataURI?
Yes, that's exactly what you would do; you'd make a LogEntry resource that states a crash dump was generated, and you use the "AdditionalDataURI" property to point to the binary, zip, or some other file with the crash details you need to extract from the system. You can use different values for DiagnosticDataType depending on what the crash dump is reporting; "Manager" would make sense if it's a crash dump of the BMC itself, but if you're collecting a crash dump of the system itself, then maybe "OS" makes more sense.
One thing to note in your example though is there should be a "MessageId" property with a properly constructed message identifier (for example: ContosoEvents.1.0.CrashDump), and a "Message" property that decodes the MessageId into something human readable. Clients will likely key off of MessageId in a log entry in order to make decisions (such as how to treat the additional data provided).