i'm one hundred percent sure that aphrodite's approval is worth a lot. i don't think she approve someone just for being attractive, it goes further. you remember that moment in the titan's curse when aphrodite says that she would love the idea of one of her daughters could break the heart of a boy like percy, well that's it. if there is someone who cares for, loves and respects their children, it will be worthy of aphrodite's approval.
for example, jason. in the lost hero everyone, including her own daughter, changes their clothes. to improve them, make them reach their full beauty, instead, with jason, she simply cleans the clothes with which he met piper and leo, she does not give him a suit or comb it, she simply cleans it and gives him clean clothes. thus showing that she approves of it, aphrodite believes that he is worthy of being her daughter's boyfriend. because that boy is "perfect", he is handsome, powerful, talented, kind, and most importantly, he believes that her daughter is the most beautiful human being in the world.
she would never approve of someone who cheats on their children or someone who treats them like shit or someone who would not die for them, she thinks her children deserve the best, and only the best gets her approval. like every mother who believes that her children deserve the best in this world.