We present detailed results of Swift observations of the nearby TeV-detected blazar Mrk 421, based on the rich archival data obtained during 2005 March-2008 June. The best fits of the 0.3-10 keV spectra were mainly obtained using the log-parabolic model, yielding low spectral curvatures expected in the case of the efficient stochastic acceleration of particles. During strong X-ray flares, the position of the synchrotron spectral energy distribution peak was beyond 8 keV for 41 spectra, while it sometimes was situated at the UV frequencies in quiescent states. The photon index at 1 keV exhibited a broad range, and the values were observed during the strong flares, hinting at the possible presence of a jet hadronic component. The spectral parameters were correlated in some periods, expected in the framework of the first- and second-order Fermi accelerations of X-ray emitting particles, as well as in the case of turbulence spectrum. The 0.3-10 keV flux and spectral parameters sometimes showed very fast variability down to the fluctuations by 6-20% in 180-960 s, possibly related to the small-scale turbulent areas containing strongest magnetic fields. X-ray and very high-energy fluxes often showed correlated variability, although several occurrences of more complicated variability patterns are also revealed, indicating that the multifrequency emission of Mrk 421 could not be generated in a single zone.