Sorry about that, I meant to say change the other query like so:

List<Recon_Detail__c> reconDetails = [Select id, Opportunity__c, Payment_Type__c From Recon_Detail__c Where Opportunity__c IN :actualOpps AND Payment_Type__c != null];

 Because this will stop the error of trying to set the Actuals field to a null value.

Okie dokie.  I tried that and now it's saying that I am dereferencing a null object on line 31.  Do I just need to add an else statement to account for the other situation at the end of the if payment type is equal to null statement before that line?

global class UpdatePaymentTypeonActual implements Database.Batchable<sObject>{
 
    //This is the query that is passed to the execute method.  It queries all of the Actuals that do not
    //have a Payment Type and find their Opportunity ID.
    
    String query = 'SELECT id, Opportunity__c, Payment_Type__c FROM Actual__c WHERE Opportunity__c != null';
 
    global database.queryLocator start(Database.BatchableContext BC) {
        return database.getQueryLocator(query);
 
    } //close start method
 
    global void execute(Database.BatchableContext BC, List<Actual__c> scope) {
        Set<Id> actualOpps = new Set<Id>();
        for (Actual__c a : scope)
        {
            actualOpps.add(a.Opportunity__c);
        }
        
       List<Recon_Detail__c> reconDetails = [Select id, Opportunity__c, Payment_Type__c From Recon_Detail__c Where Opportunity__c IN :actualOpps AND Payment_Type__c != null];
        
        Map<Id, Recon_Detail__c> rdMap = new Map<Id, Recon_Detail__c>();
        for (Recon_Detail__c rD : reconDetails)
        {
            rdMap.put(rD.Opportunity__c, rD);
        }
       
        // Iterate through the whole query of Actuals with blank Payment Types and insert Payment Type from the Recon Detail.
        for(Actual__c a : scope) {
            if(a.Payment_Type__c == null) {
               a.Payment_Type__c = rdMap.get(a.Opportunity__c).Payment_Type__c;  --failure at this line
             } //close if statement
        } //close for-loop
 
        try {
            update scope;
        } catch (system.dmlexception e) {
            System.debug('Scope not updated: ' + e);
        }
 
    } //close execute method
 
    global void finish(Database.BatchableContext BC) {
         
        AsyncApexJob a = [Select Id, Status, NumberOfErrors, JobItemsProcessed,
            TotalJobItems, CreatedBy.Email
            from AsyncApexJob where Id =
            :BC.getJobId()];
 
        // Create and send an email with the results of the batch.
        Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
 
        mail.setToAddresses(new String[] {a.CreatedBy.Email});
        mail.setReplyTo('rachelbr@angieslist.com');
        mail.setSenderDisplayName('Salesforce');
        mail.setSubject('Payment Type Batch Apex Load is' + a.Status);
        mail.setPlainTextBody('The batch apex job processed ' + a.TotalJobItems +
        ' batches with ' + a.NumberofErrors + ' failures.');
 
        Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });
 
    } //close finish method
} //close class