The ubiquity of M dwarf stars combined with their low masses and luminosities make them prime targets in the search for nearby, habitable exoplanets. We investigate the effects of starspot-induced radial velocity (RV) jitter on detection and characterization of planets orbiting M dwarfs. We create surface spot configurations with both random spot coverage and active regions. Synthetic stellar spectra are calculated from a given spot map, and RV measurements are obtained using cross-correlation technique. We add the RV signal of an orbiting planet to these jitter measurements, and reduce the data to 'measure' the planetary parameters. We investigate the detectability of planets around M dwarfs of different activity levels, and the recovery of input planetary parameters. When studying the recovery of the planetary period we note that while our original orbital radius places the planet inside the habitable zone (HZ) of its star, even at a filling factor of 2 per cent a few of our measurements fall outside the 'conservative HZ'. Higher spot filling factors result in more and higher deviations. Our investigations suggest that caution should be used when characterizing planets discovered with the RV method around stars that are (or are potentially) active.