the problems that could arise are for example the differences between religions, if they have different religions then it could become a problem when marrying because the would not be able to do certain things like in the movie where toula and ian could not marry in the church and toula´s family was not happy with this fact ian had to convert to the greek orthodox church just so they could marry in the church.
another problem could be the language the speak for example a have a relative that lives in orlando she lives with her mom and the rest of her family there and she married an american the problem lies when they have reunions with the family because her mom does not speak english and when the family is together they all speak spanish  so he can not talk to anyone because he does not understand what are they saying.
but if a couple love each other they will find a way of solving their problems, just like in the movie.