このmysqlコードはあなたのために働くはずです：
// Today
AND DATE(from_unixtime(comment_date)) = CURRENT_DATE
// Yesterday
AND DATE(from_unixtime(comment_date)) = DATE_SUB(CURRENT_DATE,INTERVAL 1 DAY)
// This week
AND YEARWEEK(from_unixtime(comment_date), 1) = YEARWEEK(CURRENT_DATE, 1)
// This month
AND YEAR(from_unixtime(comment_date)) = YEAR(CURRENT_DATE)
AND MONTH(from_unixtime(comment_date)) = MONTH(CURRENT_DATE)