We have performed comprehensive studies of optical, thermoelectric and electrical properties of Mg doped InN with varying Mg doping levels and sample thicknesses. Room temperature photoluminescence spectra show a Mg acceptor related emission and the thermopower provides clear evidence for the presence of mobile holes. Although the effects of the hole transport are clearly observed in the temperature dependent electrical properties, the sign of the apparent Hall coefficient remains negative in all samples. We show that the standard model of two electrically well connected layers (n-type surface electron accumulation and p-type bulk) does not properly describe Hall effect in p-type InN.