I think the only problem is making sure that you don't find a third world chick who wants to move to America. Also, from what I understand marriages in a lot of foreign countries don't hold water in the US or UK. I met a Brit who joked that he would have no problem marrying a Thai woman since the Thai Buddhist wedding is not considered a legal marriage by his government.
Probably the worst thing that can happen is your US wife finds out and takes you to the cleaners.
Probably the worst thing that can happen is your US wife finds out and takes you to the cleaners.