Trovato il problema. Utilizzavo 'arguments' come variabile che deduco sia una parola chiave. Da qui tutti i problemi.
Ho fatto così ad esempio e funziona:

Codice PHP:
                        // Salva
                        
$('a[href="save"]').click(function(event) {

                            
event.preventDefault();

                            var 
primary_save = $(this).attr('id');

                            
//var arguments = new Array();
                            //arguments["action"] = "save";
                            
var argomenti 'action=save';
                            
//var argomenti = {'action':'save'}

                            
$.each($(this).closest('tr').children('td.edit'), function() {
                                var 
value = $(this).children('input').val();
                                var 
name = $(this).attr('headers');
                                
argomenti += '&'+name+'='+value;
                                
//arguments['"'+name+'"'] = '"'+value+'"';
                                //alert(name);
                                //alert(value);
                                
                                
console.debug(argomenti);
                            });
                            
//alert(arguments["name"]);
                            
                            
console.debug(argomenti);
                            
                            
                        });