  Forward and backscattering play an exceptional role in the physics of
two-dimensional interacting fermions. In a Fermi liquid, both give rise to a
non-analytic $\omega^2 \log(\omega)$ form of the fermionic scattering rate at
second order in the interaction. Here we argue that higher powers of
$\log(\omega)$ appearin the backscattering contribution at higher orders. We
show that these terms come from "planar" processes, which are effectively
one-dimensional. This is explicitly demonstated by extending a Fermi liquid to
the limit of $N \gg 1$ fermionic flavors, when only planar processes survive.
We sum the leading logarithms for the case of a 2D Fermi liquid near a nematic
transition and obtain an expression for the scattering rate at $T=0$ to all
orders in the interaction. For a repulsive interaction, the resulting rate is
logarithmically suppressed, and the result is valid down to $\omega = 0$. For
an attractive interaction, the ground state is an $s$-wave superconductor with
a gap $\Delta_0$. We show that in this case the scattering rate increases as
$\omega$ is reduced towards $\Delta_0$. At $\omega \geq \Delta_0$, the behavior
of the scattering rate is rather unconventional as many pairing channels
compete near a nematic critical point, and $s$-wave wins only by a narrow
margin. We take superconductivity into consideration and obtain the scattering
rate also at smaller $\omega \simeq \Delta_0$.
