We test the quality of mean field ground states for the S = 1/2 Heisenberg antiferromagnet on a Kagome lattice. These states, motivated by the large-n saddle points of Marston and Zeng, are constructed from eigenstates of single particles hopping on lattices with uniform, staggered or no magnetic fields and their BCS analogues. Short-range spin-spin correlations (up to third-nearest-neighbour) are calculated. They are compared to those obtained by Zeng and Elser from small cluster diagonalization. In all trial states certain second- and third-neighbour correlations are qualitatively distinct from the ground state. The trial state which most resembles the ground state is the projected BCS state. Deviations of second- and third-neighbour correlations from those of the actual ground state do not appear to be due to a lack of spin-Peierls order. We argue that more short-range three-sublattice Neel order should be present. Numerical results suggest a specific choice of sublattice arrangement. We also propose specific changes in two-spin correlations which would be signatures of a transition from a state of one type to another. These may be relevant for the 2.5 mK specific heat peak recently observed in helium-3 films by Greywall and Busch.