Edit in JSFiddle

//not used in this example.  one time flag, that drops its subscriptions after the first change.
ko.oneTimeDirtyFlag = function (root) {
   var _initialized;

   //one-time dirty flag that gives up its dependencies on first change
   var result = ko.computed(function () {
       if (!_initialized) {
           //just for subscriptions
           ko.toJS(root);

           //next time return true and avoid ko.toJS
           _initialized = true;

           //on initialization this flag is not dirty
           return false;
       }

       //on subsequent changes, flag is now dirty
       return true;
   });

   return result;
};

ko.dirtyFlag = function(root, isInitiallyDirty) {
    var result = function() {},
        _initialState = ko.observable(ko.toJSON(root)),
        _isInitiallyDirty = ko.observable(isInitiallyDirty);

    result.isDirty = ko.computed(function() {
        return _isInitiallyDirty() || _initialState() !== ko.toJSON(root);
    });

    result.reset = function() {
        _initialState(ko.toJSON(root));
        _isInitiallyDirty(false);
    };

    return result;
};


function Item(id, name) {
    this.id = ko.observable(id);
    this.name = ko.observable(name);
    this.dirtyFlag = new ko.dirtyFlag(this);
}

var ViewModel = function(items) {
    this.items = ko.observableArray([
        new Item(1, "one"),
        new Item(2, "two"),
        new Item(3, "three")
    ]);
    
    this.save = function() {
        alert("Sending changes to server: " + ko.toJSON(this.dirtyItems));  
    };
    
    this.dirtyItems = ko.computed(function() {
        return ko.utils.arrayFilter(this.items(), function(item) {
            return item.dirtyFlag.isDirty();
        });
    }, this);
    
    this.isDirty = ko.computed(function() {
        return this.dirtyItems().length > 0;
    }, this);
};

ko.applyBindings(new ViewModel());
<ul data-bind="foreach: items">
    <li data-bind="css: { dirty: dirtyFlag.isDirty }">
        <span data-bind="text: id"></span>
        <input data-bind="value: name" />
        <button data-bind="click: dirtyFlag.reset">Reset</button>
    </li>
</ul>

<button data-bind="enable: isDirty, click: save">Save</button>
<hr />
<h3>Just Dirty Items</h3>
<div data-bind="text: ko.toJSON(dirtyItems)"></div>
li { padding: 2px; margin: 2px; }
input { width: 75px; }
.dirty { border: solid yellow 2px; }