I learned the following form reading the paper:
(1) The ideal BMI for men is 27, which is higher than the average BMI of the online dating population and is considered to be "overweight." I previously found in the National Health Interview Survey that men who weigh 205 lbs earn the most money. The conclusion here is that men who weigh a little more than average have better social and economic outcomes.
(2) Women have three major criteria when looking for men: looks, height, and income. Women don't care as much about education (which is a proxy for intelligence). Women dislike men who have less education than themselves, but don't seem especially interested dating men with more education.
(3) Men primarily care about how women look. They don't care much about anything else. I previously wrote about how Maureen Dowd is wrong in her claim that men don't like smart women. Men like women who are good looking, they don't care about the other stuff.
(4) Everyone has observed that in white-Asian interracial couples, it is far more common that the man is white and the woman is Asian. This paper reveals the reason for this. White women aren't interested in Asian men. All races have a preference for their own race. The race preferences for white women, in declining order, are: white, Hispanic, black, Asian. Asian men are ranked at the very bottom of the average white woman's preferences. However when looking at preferences for Asian women, white men have only a very slight dispreference compared to Asian men.
(5) The best looking men benefit from a superstar effect. Men in the top 5% of looks get far more first contact emails from women than men in the top 10% but not the top 5%. This isn't the case for women. I suspect that men figure they have no chances with the hot women so they also send emails to a lot of average and even below average women. Women are more fussy when sending out first contact emails. They only want the cream of the crop. This is demonstrates the female preference for alpha males.