I think I'm stuck between a rock and a hard place and I'm hoping someone here with a bit more experience in batch classes can give me some direction.

My batch class is relatively simple: determine the max lead score across contacts within an account and update the account.

The start method is as followed:

global Database.QueryLocator start(Database.BatchableContext BC) {
		return Database.getQueryLocator([SELECT Id, Max_Lead_Score__c , (SELECT Id, mkto2__Lead_Score__c, AccountId FROM Contacts WHERE IsDeleted = false) FROM Account WHERE IsDeleted = false]);
}

global void execute(Database.BatchableContext BC, List<sObject> scope) {
        List<Account> accounts = (List<Account>) scope;        
	    Map<Id, Account> accountsForUpdate = new Map<Id, Account>();
        Id[] accountIds = new Id[]{};
	    Integer maxLeadScore;        
        
	for(Account account : accounts) {
		maxLeadScore = null;

		//Iterate through all contacts and find the max lead score
	       	if(account.Contacts.size > 0) {
	                for(Contact contact : account.Contacts) {				
        	            if(contact.mkto2__Lead_Score__c > maxLeadScore || maxLeadScore == null)
                	        maxLeadScore = (Integer)contact.mkto2__Lead_Score__c;					
                	}
    		}

		//Some contacts have a null lead score, in the event that's the only option available, populate with a 0 value on the account.
		if(maxLeadScore == null)
			maxLeadScore = 0;

		account.Max_Lead_Score__c = maxLeadScore;
		accountsForUpdate.put(account.Id, account);
	}
        
        //This is used for debug tracking - the save results array should line up
        for(Id id : accountsForUpdate.keySet())
            accountIds.add(id);

	List<Database.SaveResult> saveResults = Database.update(accountsForUpdate.values(), false);
        List<Apex_Error__c> apexErrors = new List<Apex_Error__c>();
        
        for(Integer i = 0; i < saveResults.size(); i++) {
            if(!saveResults.get(i).isSuccess()) {
                failedUpdates++;
                
                for(Database.Error error : saveResults.get(i).getErrors()) 
                	apexErrors.add(new Apex_Error__c(Apex_Class__c = 'AccountMaxContactLeadScore', Error_Record__c = accountIds.get(i), Error_Details__c = error.getMessage()));                
            }
        }
		if(apexErrors.size() > 0)
        	insert apexErrors;
}

The first issue I ran into was First error: Aggregate query has too many rows for direct assignment, use FOR loop. Fine. So I restructured my contact loop to not do the size check:

//Iterate through all contacts and find the max lead score
            for(Contact contact : account.Contacts) {				
       	        if(contact.mkto2__Lead_Score__c > maxLeadScore || maxLeadScore == null)
            	        maxLeadScore = (Integer)contact.mkto2__Lead_Score__c;					
    		}

Then I run into this error: First error: invalid query locator. Did some research, found this, restructured my code based on his advice. http://www.interactiveties.com/b_batch_apex_invalid_query_locator.php#.VNPK953F-4J
 

for(SObject s : scope) {
    Account account = (Account) s;
    maxLeadScore = null;

	//Iterate through all contacts and find the max lead score
	Contact[] contacts = account.getSObjects('Contacts');
        	
        if(contacts != null) {
                for(Contact contact : contacts) {				
                    if(contact.mkto2__Lead_Score__c > maxLeadScore || maxLeadScore == null)
                        maxLeadScore = (Integer)contact.mkto2__Lead_Score__c;					
                }
    	}

Then I got First error: Aggregate query has too many rows for direct assignment, use FOR loop. So similar to the first method, I remove the check for nulls. Then I get null pointer errors.

So I tried removing the subquery in the start method and then doing a direct query in the excute method and I get First error: Too many query rows: 50001 - which means I have to use the subquery method.

Any advice on how to get this optimized to hit zero errors?