This page lists various harms to immigrant-receiving countries that are perceived as being due to the increased heterogeneity in terms of ethnicity, race, culture, and other aspects. Note that these arguments are not about the inferiority of immigrants but rather about intrinsic problems with heterogeneity. For arguments that are specifically about immigrant characteristics, see here.
Also closely related are assimilation problems.
Here are some of the claimed harms resulting from heterogeneity: