Aims. We present numerically calculated, disk-integrated, spectropolarimetric signals of starlight that is reflected by vertically and horizontally inhomogeneous gaseous exoplanets. We include various spatial features that are present on Solar System's gaseous planets: belts and zones, cyclonic spots, and polar hazes, to test whether such features leave traces in the disk-integrated fux and polarization signals. Methods. Broadband flux and polarization signals of starlight that is reflected by gaseous exoplanets are calculated using an efficient, adding-doubling radiative transfer code, that fully includes single and multiple scattering and polarization. The planetary model atmospheres are vertically inhomogeneous and can be horizontally inhomogeneous, and contain gas molecules and/or cloud and/or aerosol particles.Results. The broadband flux and polarization signals are sensitive to cloud top pressures, although in the presence of local pressure differences, such as in belts and clouds, the flux and polarization phase functions have similar shapes as those of horizontally homogeneous planets. Fitting flux phase functions of a planet with belts and zones using a horizontally homogeneous planet could theoretically yield cloud top pressures that differ by a few hundred mbar from those derived from fitting polarization phase functions. In practice, however, observational errors and uncertainties in cloud properties would make such a fit unreliable. A cyclonic spot like Jupiter's Great Red Spot, covering a few percent of the disk, located in equatorial regions, and rotating in and out of the observer's view yields a temporal variation of a few percent in the broadband flux and a few percent in the degree of polarization. Polar hazes leave strong traces in the polarization of reflected starlight in spatially resolved observations, especially seen at phase angles near 90 • . Integrated across the planetary disk, polar hazes that cover only part of the planetary disk, change the broadband degree of polarization of the reflected light by a few percent. Such hazes have only small effects on locally reflected broadband fluxes and negligible effects on disk-integrated broadband fluxes. Conclusions. Deriving the presence of belts and zones in the atmospheres of gaseous exoplanets from broadband flux and polarization observations will be extremely difficult. Cyclonic spots could leave temporal changes in the broadband flux and polarization signals of a few percent. Polar hazes that cover a fraction of the planetary disk, and that are composed of small, Rayleigh scattering particles, change the broadband degree of polarization by at most a few percent.