Structural and viscoelastic properties of slightly interconnected polymer networks immersed in a solvent have been studied in two cases: when the polymer network is building up and when the polymer network is shrinking stepwise in a controlled way. To accomplish this goal, the mean square displacement (MSD) of embedded microspheres in the polymer network was measured as a function of time, with diffusive wave spectroscopy. Particle motion was analyzed in terms of a model, based on a Fokker-Planck type equation, developed for describing particles in Brownian motion within a network that constrain their movement. The model reproduces well the experimental features observed in the MSD vs t curves. The variation of the parameters describing the structure of the network can be understood as the polymerization comes about, and also after the successive volume contractions. In addition, from the MSD curves, the complex shear moduli were obtained in a wide range of frequencies when the network is building up, and at the different shrinking states of the network. Our microrheological results give an insight about the dynamics of embedded particles in slightly interconnected networks, which were also compared with similar results for polymers without interconnections and polymer gels.