  We analyze quantum fluctuation effects at the onset of charge or spin density
wave order with a $2k_F$ wave vector $\mathbf{Q}$ in two-dimensional metals --
for the special case where $\mathbf{Q}$ connects a pair of hot spots situated
at high symmetry points of the Fermi surface with a vanishing Fermi surface
curvature. We compute the order parameter susceptibility and the fermion
self-energy in one-loop approximation. The susceptibility has a pronounced peak
at $\mathbf{Q}$, and the self-energy displays non-Fermi liquid behavior at the
hot spots, with a linear frequency dependence of its imaginary part. The real
part of the one-loop self-energy exhibits logarithmic divergences with
universal prefactors as a function of both frequency and momentum, which may be
interpreted as perturbative signatures of power laws with universal anomalous
dimensions. As a result, one obtains a non-Fermi liquid metal with a vanishing
quasiparticle weight at the hot spots, and a renormalized dispersion relation
with anomalous algebraic momentum dependencies near the hot spots.
