Electronic and nuclear spins of shallow donors in silicon are particularly attractive among the solid-state systems considered for quantum information storage and processing. Shallow donor exchange gates are frequently invoked to preform two-qubit operations for these spin qubits. Careful analysis of the feasibility of such operations demands realistic descriptions of the underlying electronic structure in Si. Intervalley interference between the conduction-band-edge states of Si leads to oscillatory behavior in the donor-pair exchange J. We calculate the exchange coupling for two donors within the Heitler-London approach and show that, if the donors can be placed at substitutional sites precisely along the  crystal direction, the oscillatory behavior of J may be essentially ignored in practice. However, small uncertainties in the relative positioning-between 1-5 nm-with respect to this ideal direction lead to a broad distribution of J values peaked at J∼0, posing severe limitations in the nanofabrication of shallow donor arrays and exchange gates in Si.