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The issue is that if you have wheels/tires of unequal diameter on a driving axle, it can cause abnormal wear on the differential over time. I wouldn't put an old tire and a new tire on the same axle, however if dvdswanson says it okay, you're probably good to go.
You should consider laxman's point as well. I've had similar experiences. You didn't indicate why you are replacing the tire, but if it is for some defect realted problem, then you can expect issues from the other tires eventually.
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