So, if Paul references a portion of Leviticus in support of an argument, that gives license to ignore the parts which were not referenced? On what basis?

The issue with the homosexuality argument is that Paul's argument looks directly to Leviticus for authority, not to the teachings of Christ. Hence it would seem to be a strong argument to the effect that people should try to follow the Levitican code in its entirety. This means not wearing cotton-poly blend clothes, breeding hybrid crops (assuming that this extends to transgenic crops as well) and the like.

While there are sound arguments to suggest that the bit of eating kosher need not be a part of Christian tradition anymore, the rest of the Levitican code would seem to apply as per Paul's references relating to homosexuality.