We use scanning tunneling microscopy and spectroscopy under ultrahigh vacuum and down to 1.7 K to study the local variations of the chemical potential on the surface of the topological insulator (Bi1-xSbx)(2)Te-3 thin films (thickness 7-30 nm) with varying Sb concentration x, to gain insight into the charge puddles formed in thin films of a compensated topological insulator. We found that the amplitude of the potential fluctuations, Gamma, is between 5 and 14 meV for quasi-bulk-insulating films and about 30-40 meV for bulk-insulating films. The length scale of the fluctuations, lambda, was found to span the range of 13-54 nm, with no clear correlation with Gamma. Applying a magnetic field normal to the surface, we observe the condensation of the two-dimensional topological surface state into Landau levels and find a weak but positive correlation between Gamma and the spectral width of the Landau-level peaks, which suggests that quantum smearing from drift motion is the source of the Landau-level broadening. Our systematic measurements give useful guidelines for realizing (Bi1-xSbx)(2)Te-3 thin films with an acceptable level of potential fluctuations. In particular, we found that x approximate to 0.65 realizes the situation where Gamma shows a comparatively small value of 14 meV and the Dirac point lies within similar to 10 meV of the Fermi energy.