  An extensive study of the magnetic properties of FeTe$_{0.7}$Se$_{0.3}$
crystals in the superconducting state is presented. We show that weak
collective pinning, originating from spatial variations of the charge carrier
mean free path ($\delta l$ pinning), rules in this superconductor. Our results
are compatible with the nanoscale phase separation observed on this compound
and indicate that in spite of the chemical inhomogeneity spatial fluctuations
of the critical temperature are not important for pinning. A power law
dependence of the magnetization vs time, generally interpreted as signature of
single vortex creep regime, is observed in magnetic fields up to $8 ~ T$. For
magnetic fields applied along the c axis of the crystal the magnetization
curves exhibit a clear peak effect whose position shifts when varying the
temperature, following the same dependence as observed in
YBa$_2$Cu$_3$O$_{7-\delta}$. The time and temperature dependence of the peak
position has been investigated. We observe that the occurrence of the peak at a
given magnetic field determines a specific vortex configuration that is
independent on the temperature. This result indicates that the influence of the
temperature on the vortex-vortex and vortex-defect interactions leading to the
peak effect in FeTe$_{0.7}$Se$_{0.3}$ is negligible in the explored range of
temperatures.
