Do Pluto and Charon have unusual Lagrange points? The usual examples of Lagrange points one most commonly encounters, Sun-Earth  and Earth-Moon Lagrange points, are examples of 3-body problems where $M_1\gg M_2\gg M_3$. The Pluto-Charon system, however, are much closer in their relative masses, so much so that their barycenter is outside Pluto's surface. From Wikipedia:


  Pluto and Charon are sometimes considered a binary system because the barycenter of their orbits does not lie within either body. The IAU has not formalized a definition for binary dwarf planets, and Charon is officially classified as a moon of Pluto.


How does this affect the orbital stability of the five Pluto-Charon Lagrange points?
The L1, L2, and L3 points are unstable in any orbital system. (source)

The L4 and L5 points of a pair of bodies are only stable if the larger of the bodies is at least 25 times as massive than the smaller (source).  The ratio of the Pluto/Charon system is only 8.7.  Because of this, none of the Lagrange points are stable, and an object orbiting at any of them will require active station-keeping to compensate for perturbations in the orbit.