Populating a Junction Table
Try a Cartesian or cross join.  You can test the select clause separately to ensure it selects the desired data before adding it into the insert.

INSERT INTO EPISODE_CAST (episode_id, cast_member_id)
SELECT  episode.id AS episode_id,
        cast_member.id AS cast_member_id
FROM EPISODE CROSS JOIN CAST_MEMBER 
WHERE show_number BETWEEN 1 AND 550
AND   person_name='John Smith';