The major criticism of cultural globalization is that it leads to the domination of some cultural traditions by others. This can lead even to the obliteration of certain cultural traditions, typically those of poorer, less dominant countries.
As the cultural globalization progresses, the people of the world tend to have a much more homogeneous culture. You have (as in the economist.com article below) people from a place like Cambodia who are very into bands from South Korea who sing music that is essentially the same as pop music from the West. This sort of thing takes away from cultural diversity. It destroys the cultural traditions of Cambodia because people are no longer listening to traditional types of music.
Some people see this as a bad thing because it takes away from our cultural diversity.