The effect of the limited alignment of hydrated molecules is considered in a laser-aligned molecular beam, on diffraction patterns taken from the beam. Simulated patterns for a protein beam are inverted using the Fienup-Gerchberg-Saxton phasing algorithm, and the effect of limited alignment on the resolution of the resulting potential maps is studied. For a typical protein molecule (lysozyme) with anisotropic polarizability, it is found that up to 1 kW of continuous-wave near-infrared laser power (depending on dielectric constant), together with cooling to liquid-nitrogen temperatures, may be needed to produce sufficiently accurate alignment for direct observation of the secondary structure of proteins in the reconstructed potential or charge-density map. For a typical virus (TMV), a 50 W continuous-wave laser is adequate for subnanometre resolution at room temperature. The dependence of resolution on laser power, temperature, molecular size, shape and dielectric constant is analyzed.