Magento – How to add widgets to specific pages in magento

First, here is why you get that error.
The mass action block button has this onclick event.

$this->getJsObjectName() . ".apply()"

Digging deeper in the methods the code above translates into

{parent_block_id}_massactionJsObject.apply();

(For a widget chooser the parent block id is some random hash but that's not important). The idea is that the object above does not exist.
Now the (possible) solution. Change the mass action block only for your widget chooser. For this create a new class:

<?php 
class Manners_Widgets_Block_Catalog_Product_Massaction extends Mage_Adminhtml_Block_Widget_Grid_Massaction{
    public function getApplyButtonHtml()
    {
        return $this->getButtonHtml($this->__('Submit'), "alert('Doh!')");//add this your js function that should do the magic.
    }
}

Now tell your grid to use this new mass action block. For this add int the class Manners_Widgets_Block_Catalog_Product_Widget_Chooser this method:

protected function _construct(){
    parent::_construct();
    $this->setMassactionBlockName('manners_widgets/catalog_product_massaction');
}

Now when you click on the "submit" button you will get an alert and no errors.
Change the alert in the code above with your actions.

Short answer: You cannot.

Workaround 1:
In the 'Page' dropdown are listed all the layout handles that have a <label> tag inside them. For example:

<cms_page translate="label">
    <label>CMS Pages (All)</label> 
    ...
</cms_page>

What you can do is to create a new layout handle, it can be empty, just make sure it has a label. Then add a new column on the cms/page entity (yes/no). Something like 'Use my new handle'. Then implement an Observer that loads your handle for the pages that have that attribute set to 'Yes' (since you cannot use <update handle=".." /> in the admin custom layout xml for pages). Now all your widgets linked to that layout handle will be displayed on the pages that use it.
If you want to have more than one of these custom handles then just replace the 'yes/no' dropdown with a select (or multiselect) with the layout handle you created and modify the observer to apply the handles selected for that page.
I know it's a bit 'ugly' but it should work.

edit

Possibile Implementation (as in categories)

For categories is a little different. If you want to add a similar process for cms pages, start with adding the cms pages option here: Mage_Widget_Block_Adminhtml_Widget_Instance_Edit_Tab_Main_Layout::_getDisplayOnOptions(). Then in the same class add a new option in getDisplayOnContainers(). Then see what js you can add in app/design/adminhtml/default/default/template/widget/instance/edit/layout.phtml. I would go with the additional layout handle approach. Seams cheaper.