What should you do?
1) I remind everyone of the common goal; they must reach a goal, therefore they should try to understand each other.
One can do whatever he/she wants, he/she will never obtain much unless they understand they need the will to work together without paying attention to cultural details.
2) In general terms, a homogeneous team is going to reach better results; I know this is going to sound out-of-the-main-flow but that is the truth.
Nowadays, diversity is a must; nonetheless, it creates problems, no way.
One may tell people how wonderful working with other cultures is, but in some weeks at most problems will arise between people.
For instance, take the habit of not using handkerchiefs (in thoser cultures, it would be disrespectful): people understand the real meaning, nonetheless there is always someone who feel “disturbed”. Obviously, the vice versa is true. The sum of a lot of little things is usually going to create unseen tensions.
Therefore, you should constantly be alert: immediately deal with signs of cultural misunderstanding.