  While multiband systems are usually considered for flat-band physics, here we
study one-band models that have flat portions in the dispersion to explore
correlation effects in the 2D repulsive Hubbard model in an intermediate
coupling regime. The FLEX+DMFT~(the dynamical mean-field theory combined with
the fluctuation exchange approximation) is used to show that we have a
crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band
filling is varied, which triggers a crossover from triplet to singlet pairings
with a peculiar filling dependence that is dominated by the size of the flat
region in the dispersion. A curious manifestation of the flat part appears as
larger numbers of nodal lines associated with pairs extended in real space. We
further detect non-Fermi liquid behavior in the momentum distribution function,
frequency dependence of the self-energy and spectral function. These indicate
correlation physics peculiar to flat-band systems.
