The thermodynamic and mechanical properties of graphitic systems are strongly dependent on the shear elastic constant C44. Using state-of-the-art density functional calculations, we provide the first complete determination of their elastic constants and exfoliation energies. We show that stacking misorientations lead to a severe lowering of C44 of at least one order of magnitude. The lower exfoliation energy and the lower C44 (more bending modes) suggest that flakes with random stacking should be easier to exfoliate than the ones with perfect or rhombohedral stacking. We also predict ultralow friction behaviour in turbostratic graphitic systems.