A: 

After some experimentation, I determined that I could achieve the desired result by subscribing to the MailItem's Close event rather than the Inspector's Close event. I now have a MailItemEventHandler class that handles all MailItem events:

public class MailItemEventHandler {

    public void AttachmentAdd(Variant[] arguments) {
        System.out.println("AttachmentAdd");
    }

    public void AttachmentRead(Variant[] arguments) {
        System.out.println("AttachmentRead");
    }

    public void AttachmentRemove(Variant[] arguments) {
        System.out.println("AttachmentRemove");
    }

    public void BeforeAttachmentAdd(Variant[] arguments) {
        System.out.println("BeforeAttachmentAdd");
    }

    public void BeforeAttachmentPreview(Variant[] arguments) {
        System.out.println("BeforeAttachmentPreview");
    }

    public void BeforeAttachmentRead(Variant[] arguments) {
        System.out.println("BeforeAttachmentRead");
    }

    public void BeforeAttachmentSave(Variant[] arguments) {
        System.out.println("BeforeAttachmentSave");
    }

    public void BeforeAttachmentWriteToTempFile(Variant[] arguments) {
        System.out.println("BeforeAttachmentWriteToTempFile");
    }

    public void BeforeAutoSave(Variant[] arguments) {
        System.out.println("BeforeAutoSave");
    }

    public void BeforeCheckNames(Variant[] arguments) {
        System.out.println("BeforeCheckNames");
    }

    public void BeforeDelete(Variant[] arguments) {
        System.out.println("BeforeDelete");
    }

    public void Close(Variant[] arguments) {
        System.out.println("Close");
    }

    public void CustomAction(Variant[] arguments) {
        System.out.println("CustomAction");
    }

    public void CustomPropertyChange(Variant[] arguments) {
        System.out.println("CustomPropertyChange");
    }

    public void Forward(Variant[] arguments) {
        System.out.println("Forward");
    }

    public void Open(Variant[] arguments) {
        System.out.println("Open");
    }

    public void PropertyChange(Variant[] arguments) {
        System.out.println("PropertyChange");
    }

    public void Read(Variant[] arguments) {
        System.out.println("Read");
    }

    public void Reply(Variant[] arguments) {
        System.out.println("Reply");
    }

    public void ReplyAll(Variant[] arguments) {
        System.out.println("ReplyAll");
    }

    public void Send(Variant[] arguments) {
        System.out.println("Send");
    }

    public void Unload(Variant[] arguments) {
        System.out.println("Unload");
    }

    public void Write(Variant[] arguments) {
        System.out.println("Write");
    }

}

I subscribe to the events using:

Object outlook = new ActiveXComponent("Outlook.Application");
Object mailItem = Dispatch.call(outlook, "CreateItem", 0).getDispatch();

MailItemEventHandler eventHandler = new MailItemEventHandler();
new DispatchEvents((Dispatch) mailItem, eventHandler);

I don't know much about COM, but it appears that there is something wrong with the Inspector object registration...

Adam Paynter