We investigate in detail the quantum fluctuations in the quantum holographic teleportation protocol that we recently proposed [11]. This protocol implements a continuous variable teleportation scheme that enables the transfer of the quantum state of spatially multimode electromagnetic fields, preserving their quantum correlations in space-time, and can be used to perform teleportation of 2D optical images. We derive a characteristic functional, which provides any arbitrary spatio-temporal correlation function of the teleported field, and calculate the fidelity of the teleportation scheme for multimode Gaussian input states. We show that for multimode light fields one has to distinguish between a global and a reduced fidelity. While the global fidelity tends to vanish for teleportation of fields with many degrees of freedom, the reduced fidelity can be made close to unity by choosing properly the number of essential degrees of freedom and the spatial bandwidth of the EPR beams used in the teleportation scheme.