男癖の悪さ 'bad taste in men / man-chasing habit' uses the compound 男癖 (男 'man' + 癖 'habit/tendency'). あきれて物が言えない 'so appalled one can't speak' is a set expression for being rendered speechless by someone's behavior. にはあきれて marks the topic with the emphatic には for the cause of the reaction.