MySQLでは自己相関サブクエリが使えないらしいので、内部結合を使って自分のテーブル内のカラムを集計し、別のカラムに入れる。

update_by_innerjoin

UPDATE  movie_log
INNER JOIN (
    SELECT  
        item_id,
        date,
        view + 
        (
            comment * 
            (
                (view + mylist) / (view + comment + mylist)
            ) 
        ) + mylist * 15 AS calculated_point
    FROM movie_log
) AS temp
ON  movie_log.item_id = temp.item_id
AND movie_log.date = temp.date
SET movie_log.point = calculated_point;