The primary causes of divorce, which are likely very similar across countries and cultures, are finances, lack of communication, and trust. In general, no matter how much money one earns, arguments about finances are a huge reason for eventual divorce. This plays an even bigger role in international divorce, since some countries are much more lenient with hiding assets.
The U.S. has stringent laws to ensure assets are made known in order to equitably settle any dispute over money as well as provide for alimony or child care when necessary. Because international laws vary so widely concerning divorce, there is a significant risk that an American citizen who marries a foreigner would be unaware of assets that are hidden in the foreign country. And even if one is aware of those assets, may not legally be able to lay claim to them.
In addition, the same issues tend to arise with regards to child custody and child support. Some countries do not participate in the Hague Convention, and therefore may put children at risk for abduction by a parent with limited ability to try to repatriate the child. In addition, countries in general tend to favor towards one side versus another (e.g. father versus mother). The US overall heavily favors the mother, while a place like Japan does the opposite.
The relative lack of discrete laws governing international marriage and divorce should give pause to those considering marrying a foreigner. Although it is always difficult to speak of topics such as divorce while one is in the process of marrying, protecting one’s assets and children requires investigating the laws of the spouse’s country.