  Mexican-hat dispersion of band electrons in two-dimensional materials
attracts a lot of interest, mainly due to the Van Hove singularity of the
density of states near the band edge. In this paper, we show that there is one
more feature of such a dispersion, which also leads to nontrivial effects. It
consists in the fact that the sign of the effective mass in the momentum space
near the central extremum is opposite to the sign of the mass outside this
region. For this reason, any localized potential that repels quasiparticles in
the outer region attracts quasiparticles in the central region and thereby
creates quasi-bound states. We study these states in the case when the
Mexican-hat dispersion is formed due to the hybridization of the inverted
electron and hole bands, and the potential is created by a point defect. The
energy and width of the resonance of the local density of states corresponding
to a quasi-bound state are found, and it is shown that, under certain
conditions, a quasi-bound state can transform into a bound state in a continuum
of band states. The presence of quasi-bound states leads to nontrivial effects
in the spin-dependent scattering of electrons. Due to the quasi-bound state,
the skew scattering is strongly enhanced for electrons with energy near the
resonance, and the skewness angle varies over a wide range depending on the
energy. In addition, in a certain energy range, a nontrivial effect of
scattering suppression appears in the direction opposite to the skewness angle.
