  We present multi-wavelength observations and modeling of the exceptionally
bright long $\gamma$-ray burst GRB 160625B. The optical and X-ray data are
well-fit by synchrotron emission from a collimated blastwave with an opening
angle of $\theta_j\approx 3.6^\circ$ and kinetic energy of $E_K\approx
2\times10^{51}$ erg, propagating into a low density ($n\approx 5\times10^{-5}$
cm$^{-3}$) medium with a uniform profile. The forward shock is sub-dominant in
the radio band; instead, the radio emission is dominated by two additional
components. The first component is consistent with emission from a reverse
shock, indicating an initial Lorentz factor of $\Gamma_0\gtrsim 100$ and an
ejecta magnetization of $R_B\approx 1-100$. The second component exhibits
peculiar spectral and temporal evolution and is most likely the result of
scattering of the radio emission by the turbulent Milky Way interstellar medium
(ISM). Such scattering is expected in any sufficiently compact extragalactic
source and has been seen in GRBs before, but the large amplitude and long
duration of the variability seen here are qualitatively more similar to extreme
scattering events previously observed in quasars, rather than normal
interstellar scintillation effects. High-cadence, broadband radio observations
of future GRBs are needed to fully characterize such effects, which can
sensitively probe the properties of the ISM and must be taken into account
before variability intrinsic to the GRB can be interpreted correctly.
