Let \(G\) be an abelian group and let \(G^\#\) denote \(G\) equipped with the Bohr topology. If \(G = Z\), the additive group of the integers, and \(A\) is a Hadamard set in \(Z\), it is shown that (i) \(A - A\) has 0 as its only limit point in \(Z^\#\), (ii) no Sidon subset of \(A - A\) has a limit point in \(Z^\#\), (iii) \(A - A\) is a \(\Lambda (p)\) set for all \(p < \infty\). These results are applied to describe some explicit examples.