My personal take is:
Only marry someone who is either an American citizen (born or naturalized), or who has had her permanent residence for at least two years. It takes 5 years as a permanent resident to become a citizen for someone who is not married to an American citizen, and 3 years as a permanent resident for someone who is married to an American citizen. Take away the possibility for a fast track to citizenship, and you cut down on fraud.
If she says she can't get a passport or a smartphone or plane tickets, don't believe her.
Many foreign women picked the US before they picked you. Consider why. Here's an example of why some women would prefer to marry American men:
So, to break it down:
1) Independence over being a housewife.
2) Don't have to cook/do laundry for him.
3) He's less likely to cheat.
4) Less complaints about being overweight.
5) We're more care-free than reserved.
6) We're more equality-minded.
In other words, if she wants more independence, and isn't gravitating towards being what is traditionally considered a good housewife (cooking/cleaning, etc), and isn't gravitating towards quiet men, and is likelier to let herself go in the weight department once married, and isn't as much of a "yes" woman with her husband, that's the kind of woman that wants to come here. What I have noticed about men who seek after foreign women is they want the opposite in a woman, and tend to be not the most social of men. So this can be a recipe for disaster.
The most serious of these of course, is the independence - an American feminist at least knows that marriage isn't a vehicle to independence, it's the opposite. Your spouse is at least as important as your dreams, and ideally, people would marry around compatible dreams. And they still have to give after that - if you have a relative that dies right when there's supposed to be an extended family visit to your in-laws that your spouse has been looking forward to for months, you two will have to give a bit on what to do and where to go. But consider the woman who wants independence and sees marriage to an American man as the fast track to getting it. She may or may not leave him right after she gets it, but what's going to cause real tension is she chose the US before she chose him, and she wants to study here and work there and live in this other place and the man she marries is along for the ride, or he's in the way. That's going to be a miserable marriage.
Also, let's not forget that culture clash as to how to live at home is a very real thing.
Most of this comes from different assumptions about what home life is supposed to be. The differences here seem more pronounced than what is normal between two Americans. Unlike this couple, a friend of mine married a Chinese woman for just under two years and then they divorced. I wonder how much of this was a factor in that.