The bad side to a multicultural society is that it diminishes the country as its culture is dialuted. England for example is very multicultural but traditional English places has been mixed with foreign take-aways.
The countries may also changes for tourists e.g. traditional dances will be performed to tourists and edited to suit tourists, loosing the dances purity and original meaning.
Believing in certain values and traditions when you are in a country which has the opposite ideals, can sometimes cause conflict. For example if a group of people immigrated to a country and decided the elders of the group should decide punishments for crimes done by people in the group and not letting police get involved.