Cprocessing,

I'm afraid you spoke too soon in calling my response brilliant as I made a rookie mistake-you need to requery the record before running the assert statements as the in-memory variables are not updated when the database is updated (a little quirk in Salesforce). Thus, adding the SOQL query lines and updating the System.assertEquals parameters accordingly should do the trick. Try this code:

@isTest
private class testDisputeStatus {

    static testMethod void myUnitTest() {
    	
   	//Create Account
   	Account testAccount = new Account(Name = 'test');
   	
   	//Insert the record
   	insert testAccount;
    
        //Create Dispute, with required account
	Dispute__c testDispute = new Dispute__c(Account__c = testAccount.Id);

	//Insert the record, this does not fire the trigger	
	insert testDispute;

	//Set resolved field to true
	testDispute.Resolved__c = true;
	
	//Update record & fire trigger, this should cause the
	//first if statement code to run
	update testDispute;

	//Query the database to refresh our dispute record variable
	Dispute__c updatedDispute1 = [SELECT Id, Status_of_Problem__c FROM Dispute__c WHERE Id = :testDispute.Id];

	//Ensure the code fired properly
	System.assertEquals(updatedDispute1.Status_of_Problem__c, 'Resolved');

	//Set resolved field to false		        
	testDispute.Resolved__c = false;

	//Update record & fire trigger, this should cause the
	//'else' code to run
	update testDispute;

	//Query the database to refresh our dispute record variable
	Dispute__c updatedDispute2 = [SELECT Id, Status_of_Problem__c FROM Dispute__c WHERE Id = :testDispute.Id];

	//Ensure the code fired properly
	System.assertEquals(updatedDispute2.Status_of_Problem__c,'Waiting for RESPONSE');

	//Insert a new conversation that looks up to the 
	//dispute record; note-you might have some required fields
	//that must be set other than what I specify here
	Conversation__c testConvo = new Conversation__c(Dispute__c = testDispute.Id);
	
	//Insert the Conversation
	insert testConvo;

	//This will now cause the Un_Actioned_Conversations field in
	//testDispute to be 1; this may fire your trigger automatically
	//but just in case let's update the record to be sure it fires
	update testDispute;
 
	//Query the database to refresh our dispute record variable
	Dispute__c updatedDispute3 = [SELECT Id, Status_of_Problem__c FROM Dispute__c WHERE Id = :testDispute.Id];
      
	//Ensure the code fired properly
	System.assertEquals(updatedDispute3.Status_of_Problem__c,'Waiting for ACTION');
        
    }
}