  The interplay between strong correlations and non-trivial topology in twisted
moir\'e systems can give rise to a rich landscape of ordered states that
intertwine the spin, valley, and charge degrees of freedom. In this paper, we
investigate the properties of a system that displays long-range
valley-polarized nematic order. Besides breaking the threefold rotational
symmetry of the triangular moir\'e superlattice, this type of order also breaks
twofold rotational and time-reversal symmetries, which leads to interesting
properties. First, we develop a phenomenological model to describe the onset of
this ordered state in twisted moir\'e systems and to explore its signatures in
their thermodynamic and electronic properties. Its main manifestation is that
it triggers the emergence of in-plane orbital magnetic moments oriented along
high-symmetry lattice directions. We also investigate the properties of the
valley-polarized nematic state at zero temperature. Due to the existence of a
dangerously irrelevant coupling $\lambda$ in the six-state clock model that
describes the putative valley-polarized nematic quantum critical point, the
ordered state displays a pseudo-Goldstone mode. Using a two-patch model, we
compute the fermionic self-energy to show that down to very low energies, the
Yukawa-like coupling between the pseudo-Goldstone mode and the electronic
degrees of freedom promotes the emergence of non-Fermi liquid behavior. Below a
crossover energy scale $\Omega^{*}\sim\lambda^{3/2}$, however, Fermi liquid
behavior is recovered. Finally, we discuss the applicability of these results
to other non-trivial nematic states, such as the spin-polarized nematic phase.
