The electrostatics and density correlations of dipolar solvent molecules in weakly charged polyelectrolyte solutions and charged gels are studied using a field-theoretical approach. For miscible dipolar solvent mixtures, an exact expression for the effective dielectric permittivity is obtained on the mean-field level, which depends upon the individual volume of each solvent species before mixing and the final volume of the mixture. If the effect of volume change is small during mixing, the dielectric permittivity is approximately equal to the volume-averaged dielectric permittivity of the individual components of the dipolar solvent mixture. It is found that the electrostatic interaction between the dipolar solvent molecules or any charged species in the polyelectrolyte solution is screened by both counterions (and co-ions if salt is added) and polyions, and there exists a total screening length for any charged species in the system which contains the contribution from the polyions. The screening from the polyions is as important as that from the counterions on the length scale of the polymer coil size. For uniaxially stretched charged gels, it is shown that there is an enhanced orientational ordering of the dipolar solvent molecules along the stretching direction, and the correlation length (r(cor)) of this enhanced orientational ordering is about the product of the total screening length (xi(-1)) due to the counterions and polyions times the square root of the dielectric constant of the medium, that is, r(cor) approximate to (epsilon(r)xi(-1))(1/2).