Workshop 201, Tutorial 4, Step 3, Apex

InvoiceUtilities.cls

global with sharing class InvoiceUtilities {

    // class method to renumber Line Items for a given Invoice number
    // returns a string that indicates success or failure
    webservice static String renumberLineItems(String invoiceName) {

    // create a copy of the target Invoice object and it's Line Items
    Invoice__c invoice = [Select i.Name, (Select Name From Line_Items__r ORDER BY Name) 
                            From Invoice__c i 
                           Where i.Name = :invoiceName LIMIT 1];

    // loop through each Line Item, renumbering as you go
    Integer i = 1;
    for (Line_Item__c item : invoice.Line_Items__r) {
      item.Name = String.valueOf(i);
      System.debug(item.Name);
      i++;
    }

    // update the Line Items in one transaction, rollback if any problems
    // and return error messages to the calling environment
    try {
      database.update(invoice.Line_Items__r);
    }
    catch (DmlException e) {
      return e.getMessage();
    }

    // on success, return a message to the calling program
    return 'Line items renumbered successfully.'; 
  }
}

Ok I found the error, here is the solution if somebody need it.
In the javascript code is the error, replace you javascript code for this:

{!REQUIRESCRIPT("/soap/ajax/25.0/connection.js")}
{!REQUIRESCRIPT("/soap/ajax/25.0/apex.js")}
var result = sforce.apex.execute("InvoiceUtilities","renumberLineItems",{"invoiceName":"{!Factura__c.Name}"});
alert(result);
window.location.reload();

Note that the paramater name is not << invoice >> like the workshop explain, is << "invoiceName" >> like the name of the parameter given to the method << renumberLineItems >>

Had the same Error Alert, glad to stumbleupon this post that helped me figure it out...

The Javascript button that use the SOAP API can call the Apex Class and transfer the String Variable into to it only when I changed the definition of the Class and Method to be global and use the webservice..

FROM:
public class InvoiceUtilities {
public static String renumberLineItems(String invoiceName) {

INTO:
global with sharing class InvoiceUtilities {
webservice static String renumberLineItems(String invoiceName) {