Comment 4 for bug 968738

A little bit more clear description:

From Pluto's surface, Charon presents one side only, as it should, but rises and sets.
From Charon's surface, Pluto appears to be in the same spot in the sky, but visibly rotates.

Either Stellarium's data on Pluto's rotation and axis is wrong (e.g. not calculated in the same epoch as Charon's orbit), or the culprit is the way natural satellite orbits are modeled in Stellarium, which breaks down with Pluto and Charon, because the barycenter of their system is outside Pluto.