Magento Grid Block has useful function for advanced filtering of a collection. It is called ‘filter_condition_callback’, and it is used in declaring a column. It takes actual collection, and callback function as parameters.

Major elements:

'filter_condition_callback' => array($this, 'filter_special_price'),

and:

public function filter_special_price($collection, $column) {
        if (!$value = $column->getFilter()->getValue()) {
            return $this;
        }
        $dateToday = Mage::app()->getLocale()->date()->toString('M/d/y');
        $this->getCollection()->addAttributeToFilter('special_price', array('neq' => ''))
            ->addAttributeToFilter('special_from_date', array('date' => true, 'to' => $dateToday))
            ->addAttributeToFilter('special_to_date', array(
                'or'=> array(
                    0 => array('date' => true, 'from' => $dateToday),
                    1 => array('is' => new Zend_Db_Expr('null')))
            ), 'left');

        return $this;

    }

All Code:

getCategory()->getProductsReadonly()) {
            $this->addColumn('in_category', array(
                'header_css_class' => 'a-center',
                'type'      => 'checkbox',
                'name'      => 'in_category',
                'values'    => $this->_getSelectedProducts(),
                'align'     => 'center',
                'index'     => 'entity_id'
            ));
        }
        $this->addColumn('entity_id', array(
            'header'    => Mage::helper('catalog')->__('ID'),
            'sortable'  => true,
            'width'     => '60',
            'index'     => 'entity_id'
        ));
        $this->addColumn('name', array(
            'header'    => Mage::helper('catalog')->__('Name'),
            'index'     => 'name'
        ));
        $this->addColumn('sku', array(
            'header'    => Mage::helper('catalog')->__('SKU'),
            'width'     => '80',
            'index'     => 'sku'
        ));
        $this->addColumn('price', array(
            'header'    => Mage::helper('catalog')->__('Price'),
            'type'  => 'currency',
            'width'     => '1',
            'currency_code' => (string) Mage::getStoreConfig(Mage_Directory_Model_Currency::XML_PATH_CURRENCY_BASE),
            'index'     => 'price'
        ));
        $this->addColumn('has_special_price', array(
            'header'    => Mage::helper('catalog')->__('Special price'),
            'width'     => '1',
            'type'      => 'checkbox',
            'index'     => 'Has special price',
            'filter_condition_callback' => array($this, 'filter_special_price'),
        ));
        $this->addColumn('position', array(
            'header'    => Mage::helper('catalog')->__('Position'),
            'width'     => '1',
            'type'      => 'number',
            'index'     => 'position',
            'editable'  => !$this->getCategory()->getProductsReadonly()
            //'renderer'  => 'adminhtml/widget_grid_column_renderer_input'
        ));

        return parent::_prepareColumns();
    }

    public function filter_special_price($collection, $column) {
        if (!$value = $column->getFilter()->getValue()) {
            return $this;
        }
        $dateToday = Mage::app()->getLocale()->date()->toString('M/d/y');
        $this->getCollection()->addAttributeToFilter('special_price', array('neq' => ''))
            ->addAttributeToFilter('special_from_date', array('date' => true, 'to' => $dateToday))
            ->addAttributeToFilter('special_to_date', array(
                'or'=> array(
                    0 => array('date' => true, 'from' => $dateToday),
                    1 => array('is' => new Zend_Db_Expr('null')))
            ), 'left');

        return $this;

    }
}