The predictions of polymer mode coupling theory for the finite size corrections to the transport coefficients of entangled polymeric systems are tested in comparison with various experimental data. It is found that quantitative descriptions of the viscosities, eta, dielectric relaxation time, tau(epsilon), and diffusion coefficients, D, of polymer melts can be achieved with two microscopic structural fit parameters whose values are in the range expected from independent theoretical or experimental information. An explanation for the (apparent) power law behaviors of eta, tau(epsilon), and D in (chemically distinct) melts for intermediate molecular weights as arising from finite size corrections, mainly the self-consistent constraint release mechanism, is given. The variation of tracer dielectric relaxation times from Rouse to reptation-like behavior upon changes of the matrix molecular weight is analyzed. Self-diffusion and tracer diffusion constants of entangled polymer solutions can be explained as well, if one further parameter of the theory is adjusted. The anomalous scaling of the tracer diffusion coefficients in semidilute and concentrated polystyrene solutions, D similar to N-2.5, is predicted to arise due to the spatial correlations of the entanglement constraints, termed "constraint porosity". Extensions of the theory to polymer tracer diffusion through poly(vinyl methyl ether) and polyacrylamide gels provide an explanation of the observation of anomalously high molecular weight scaling exponents in a range where the size of the tracer, R-g, already considerably exceeds the gel pore size, xi(g).