• campingListForm Helper - line 2. getItem() isn't a function. You must use getEvent().
• campingListFprm Helper - line 3. The variable item is being fed as a parameter, but it doesn't exist. The variable is brought in through the function, and is newItem.
• The requirement is for the submit button to call the action submitForm

<aura:component controller="CampingListController">
    <aura:handler name="init" action="{!c.doInit}" value="{!this}"/>
    
    <aura:handler name="addItem" event="c:addItemEvent" action="{!c.handleAddItem }"/>
    
    <aura:attribute name="items" type="Camping_Item__c[]"/>
    
       <!-- NEW EXPENSE FORM -->
    <div class="slds-col slds-col--padded slds-p-top--large">
        <c:campingListForm/>
    </div>
    <!-- / NEW EXPENSE FORM -->    

    <div class="slds-card slds-p-top--medium">
        <header class="slds-card__header">
            <h3 class="slds-text-heading--small">Items</h3>
        </header>
        
        <section class="slds-card__body">
            <div id="list" class="row">
                <aura:iteration items="{!v.items}" var="item">
                    <c:campingListItem item="{!item}"/>
                </aura:iteration>
            </div>
        </section>
    </div>
</aura:component>

({
    // Load items from Salesforce
	doInit: function(component, event, helper) {
    
        // Create the action
        var action = component.get("c.getItems");
    
        // Add callback behavior for when response is received
        action.setCallback(this, function(response) {
            var state = response.getState();
            if (component.isValid() && state == "SUCCESS") {
                component.set("v.items", response.getReturnValue());
            }
            else {
                console.log("Failed with state: " + state);
            }
        });
    
        // Send action off to be executed
        $A.enqueueAction(action);
	},
    handleAddItem : function (component,event,helper){
	var action = component.get("c.saveItem");
        var Item = event.getParam("item");
        var lstItems = component.get("v.items");

        lstItems.push(Item);
        component.set("v.items",lstItems);
        console.log("After:"+lstItems);
        action.setParams({"CampingItem":Item});
        action.setCallback(this,function(response){
            var state = response.getState();
                
            if (component.isValid() && state === "SUCCESS") {
                //let the magic happen
            }
         });
        $A.enqueueAction(action);   
     }
})

({
    createCamping: function(component, item) {
        var theitems = component.get("v.items");
 
        var newitem = JSON.parse(JSON.stringify(item));
 
        theitems.push(newitem);
        component.set("v.items", theitems);
        
        component.set("v.newItem",{ 'sobjectType': 'Camping_Item__c','Name': '','Quantity__c': 0,
                    'Price__c': 0,'Packed__c': false });
    },
    validateCampingItem: function(component) {
        // Simplistic error checking
        var validCamping = true;

        // Name must not be blank
        var nameField = component.find("campname");
        
        if ($A.util.isEmpty(nameField.get("v.value"))){
            validCamping = false;
            nameField.set("v.errors", [{message:"Camping name can't be blank."}]);
        } else {
            nameField.set("v.errors", null);
        }
        
        if ($A.util.isEmpty(component.find("campQty").get("v.value"))){
            validCamping = false;
            component.find("campQty").set("v.errors", [{message:"Camping Quantity can't be blank."}]);
        } else {
            component.find("campQty").set("v.errors", null);
        }
        
        if ($A.util.isEmpty(component.find("campPrice").get("v.value"))){
            validCamping = false;
            component.find("campPrice").set("v.errors", [{message:"Camping Price can't be blank."}]);
        } else {
            component.find("campPrice").set("v.errors", null);
        }
        
        return(validCamping);
    },
    createItem: function(component, item) {
        var action = component.get("c.saveItem");
        action.setParams({
            "item": item
        });
            
        action.setCallback(this, function(response) {
            var state = response.getState();
            if (component.isValid() && state == "SUCCESS") {
                var items = component.get("v.items");
                items.push(response.getReturnValue());
                component.set("v.items", items);
            }
        });
            
        $A.enqueueAction(action);
    }
})

<aura:component >
    <aura:registerEvent name="addItem" type="c:addItemEvent"/>
    
    <aura:attribute name="newItem" type="Camping_Item__c"
     default="{ 'sobjectType': 'Camping_Item__c',
                    'Name': '',
                    'Quantity__c': 0,
                    'Price__c': 0,
                    'Packed__c': false }"/>
        <!-- CREATE NEW ITEM FORM -->
    <form class="slds-form--stacked">

      <div class="slds-form-element slds-is-required">
          <div class="slds-form-element__control">
              <ui:inputText aura:id="itemname" label="Name"
                  class="slds-input"
                  labelClass="slds-form-element__label"
                  value="{!v.newItem.Name}"
                  required="true"/>

          </div>
     </div>

     <div class="slds-form-element slds-is-required">
          <div class="slds-form-element__control">
              <ui:inputNumber aura:id="quantity" label="Quantity"
                  class="slds-input"
                  labelClass="slds-form-element__label"
                  value="{!v.newItem.Quantity__c}"
                  required="true"/>

          </div>
      </div>

      <div class="slds-form-element">
          <div class="slds-form-element__control">
              <ui:inputCurrency aura:id="price" label="Price"
                  class="slds-input"
                  labelClass="slds-form-element__label"
                  value="{!v.newItem.Price__c}"
                  />
          </div>
      </div>

      <div class="slds-form-element">
          <ui:inputCheckbox aura:id="packed" label="Packed?"
              class="slds-checkbox"
              labelClass="slds-form-element__label"
              value="{!v.newItem.Packed__c}"/>
      </div>

      <div class="slds-form-element">
          <ui:button label="Create Camping Item"
              class="slds-button slds-button--brand"
              press="{!c.submitForm}"/>
      </div>

    </form>
    <!-- / CREATE NEW ITEM FORM -->
</aura:component>

({
    submitForm: function(component, event, helper) {    
        if(helper.validateItemForm(component)){
            // Create the new item
            var newItem = component.get("v.newItem");
            helper.createItem(component, newItem);
        }
    }
})

({
	createItem: function(component, newItem) {
        var addItem = component.getEvent("addItem");
        addItem.setParams({ "item": newItem });
        addItem.fire();
        component.set("v.newItem",{ 'sobjectType': 'Camping_Item__c',
                        'Name': '',
                        'Quantity__c': 0,
                        'Price__c': 0,
                        'Packed__c': false });
    },
    validateItemForm: function(component) {
        // Simplistic error checking
        var validItem = true;

        // Name must not be blank
        var nameField = component.find("itemname");
        var itemname = nameField.get("v.value");
        if ($A.util.isEmpty(itemname)){
            validItem = false;
            nameField.set("v.errors", [{message:"Item name can't be blank."}]);
        } else {
            nameField.set("v.errors", null);
        }
        
        // Quantity must not be blank
        var quantityField = component.find("quantity");
        var quantity = nameField.get("v.value");
        if ($A.util.isEmpty(quantity)){
            validItem = false;
            quantityField.set("v.errors", [{message:"Quantity can't be blank."}]);
        } else {
            quantityField.set("v.errors", null);
        }
		// Price must not be blank
        var priceField = component.find("price");
        var price = priceField.get("v.value");
        if ($A.util.isEmpty(price)){
            validItem = false;
            priceField.set("v.errors", [{message:"Price can't be blank."}]);
        } else {
            quantityField.set("v.errors", null);
        }
        return (validItem);
	}
})

<aura:event type="COMPONENT">
    <aura:attribute name="item" type="Camping_Item__c"/>
</aura:event>