Independent contrasts with non-homologous traits
When you calculate the PICs of a trait, you are making a statement about how that trait evolved. The purpose of PICs is to account for phylogenetic non-independence. However, when you are comparing two analogous traits, those two traits are in fact phylogenetically independent of each other; they do not share a common origin. Thus, I think it would be an error to perform PICs on analogous traits because those traits do not share an evolutionary origin. 

How to deal with this problem would depend on the specific question you are asking. One thing to do would be to perform PICs on each trait independently on just the portion of the tree that that trait occurs so you are not comparing analogous traits.

You've probably already read this, but I recommend that anyone who hasn't check out Felsenstein's 1985 paper describing the PIC method.