Transport coefficients of small-chemical-potential quark-gluon plasmas are estimated and dissipative corrections to the scaling hydrodynamic equations for ultrarelativistic nuclear collisions are studied. The absence of heat-conduction phenomena is clarified. Lower and upper bounds on the shear-viscosity coefficient are derived. QCD phenomenology is used to estimate effects of color-electric and -magnetic shielding, and nonperturbative antiscreening. Bulk viscosity associated with the plasma-to-hadron transition is estimated within the relaxation-time approximation. Finally, effects of dissipative phenomena on the relation between initial energy density and final rapidity density are estimated.