It should not have an unpleasant smell or taste because the cigars will pick it up. The wood also should be porous so it will first absorb, then release moisture evenly, while remaining dimensionally stable. For many woods, this is a recipe for severe cupping. Spanish cedar is the traditional and best choice for a humidor. Its oils inhibit the growth of molds and mildew that destroy cigars.
Spanish cedar has a delicate aroma that is complementary, enhancing the cigar's taste.
It will ooze out of the wood, stick to your cigars and ruin them. Pieces that look sap-free can bleed many months after the humidor is finished. However, I have found little difference between them. There are ways to reduce the problem with sap. The thinner you slice the cedar, the less sap the piece will bleed later.