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"Eskimo" is considered a slur... He is part Inuit - I can see it in his face, and in the face of his children... It's subtle, but it's there.
Eskimo is only considered a slur in Greenland and Canada, it is not in Alaska and Siberian Russia.
The reason is because of the Yupik, a group distinct from the Inuit. Todd Palin is part Yupik, not Inuit.
The term Eskimo is used when referring to both Yupik and Inuit together, and often to just Yupik.