The Significance of Insignificant Results

What happens when a scientific experiment results in failure to falsify the null hypothesis? Typically negative results get filed away in a cabinet, never to be published or shared with the rest of the research committee. But what is the cost to science of this system in terms of duplicated effort? The article "Null and Void" explores some of these issues, mostly in the biological sciences. What are some of the suggested solutions posed by the author, and do you think this issue has any relevance for anthropologists?