The critical behaviour of wavefunctions at the Anderson metal-insulator transition is studied by numerical simulation, using as an example of a system with a mobility edge a two-dimensional tight-binding model with spin-orbit scattering. It is demonstrated that individual eigenstates have multifractal fluctuations of their probability density. The influence of these fluctuations on the two-particle correlations is examined via calculations of the wavevector and frequency dependence of the diffusion constant.