We consider critical eigenstates in a two dimensional quasicrystal and their evolution as a function of disorder. By exact diagonalization of finite size systems we show that the evolution of the spectral properties of a typical wavefunction is non-monotonic. That is, disorder leads to states delocalizing, until a certain crossover disorder strength is attained, after which they start to localize. This non-monotonic evolution of spatial properties of eigenstates can be observed in the anomalous dimensions of the wavefunction amplitudes, in their multifractal spectra, and in their dynamical properties. We compute the two-point correlation functions of wavefunction amplitudes and show that these follow power laws in distance and energy, consistent with the idea that wavefunctions retain their multifractal structure on a scale which depends on disorder strength. Finally dynamical properties are studied as a function of disorder. We find that the diffusion exponents do not reflect the non-monotonic wavefunction evolution. Instead, they are essentially independent of disorder until disorder increases beyond the crossover value, after which they decrease rapidly, until the strong localization regime is reached. The differences between our results and earlier studies on geometrically disordered "phason-flip" models lead us to propose that the two models are in different universality classes. We conclude by discussing some implications of our results for transport and a proposal for a Mott hopping mechanism between power law localized wavefunctions, in moderately disordered quasicrystals.