Step strain experiments and dynamic light scattering measurements are performed to characterize the dynamic behavior of an oil-in-water droplet microemulsion into which is incorporated a telechelic polymer. At sufficient droplet and polymer concentrations, above the percolation threshold, the system is viscoelastic and its dynamic structure factor consists of two steps for the relaxation of concentration fluctuations: the fast one is dominated by the diffusion but the slower one is almost independent of the wave vector. The terminal time of the stress relaxation tau (R) and the slow time of the dynamic structure factor tau (s) are both presumably controlled by the residence time of a sticker in a droplet: consistently, tau (R) and tau (s) are of the same order, they both vanish at the percolation threshold according to power laws but with different exponents. We discuss these features in terms of deviations at the transition, from the usual mean field description of the dynamics of transient networks.