  We show that the singularities in the dynamical bosonic response functions of
a generic 2D Fermi liquid give rise to universal, non-analytic corrections to
the Fermi-liquid theory. These corrections yield a $T^2$ term in the specific
heat, $T$ terms in the effective mass and the uniform spin susceptibility
$\chi_s (Q=0,T)$, and $|Q|$ term in $\chi_s (Q,T=0)$. The existence of these
terms has been the subject of recent controversy, which is resolved in this
paper. We present exact expressions for all non-analytic terms to second order
in a generic interaction $U(q)$ and show that only U(0) and $U(2p_F)$ matter.
