Get multiple columns from a select subquery
Assuming combination product_special.id, product_special.priority is unique     

 SELECT p.*, special_price,special_date
 FROM product p
 LEFT JOIN 
 (
     SELECT ps.id, ps.price as special_price, ps.`date` as special_date
     FROM product_special ps
     INNER JOIN 
     (
       SELECT id, MIN(priority) as min_priority 
       FROM product_special
       GROUP BY id
     ) ps2 
     ON (ps2.id = ps.id)
 )a ON (a.id=p.id)