NLP systems for tasks such as question answering and information extraction typically rely on statistical parsers. But the efficacy of such parsers can be surprisingly low, particularly for sentences drawn from heterogeneous corpora such as the Web. We have observed that incorrect parses often result in wildly implausible semantic interpretations of sentences, which can be detected automatically using semantic information obtained from the Web. Based on this observation, we introduce Web-based semantic filtering--a novel, domain-independent method for automatically detecting and discarding incorrect parses. We measure the effectiveness of our filtering system, called WOODWARD, on two test collections. On a set of TREC questions, it reduces error by 67%. On a set of more complex Penn Treebank sentences, the reduction in error rate was 20%.