Local dissipation-scale distributions and high-order statistics of the energy dissipation rate are examined in turbulent channel flow using very high-resolution direct numerical simulations at Reynolds numbers Reτ = 180, 381 and 590. For sufficiently large Reτ , the dissipation-scale distributions and energy dissipation moments in the channel bulk flow agree with those in homogeneous isotropic turbulence, including only a weak Reynolds-number dependence of both the finest and largest scales. Systematic, but Reτ -independent, variations in the distributions and moments arise as the wall is approached for y+ 100. In the range 100 textless y+ textless 200, there are substantial differences in the moments between the lowest and the two larger values of Reτ . This is most likely caused by coherent vortices from the near-wall region, which fill the whole channel for low Reτ .