We have studied phase transitions in multiferroic Ni3V2O8, through dielectric measurements and by investigating the effects of Zn doping. The divergence of the dielectric constant near TL = 6.4 K can be approximately fit by power law behaviour, but exhibits different critical exponents above and below TL. The two higher temperature magnetic transitions in (Ni1-xZnx)3V2O8, are strongly suppressed as the Zn doping fraction x is increased. The rates of the suppression of both TH and TL with x are consistent with two-dimensional spin systems, with the suppression of TH consistent with Ising spins and the suppression of TL consistent with Heisenberg spins.