A growing volume of heritage data is being digitized and made available as text via optical character recognition (OCR). Scholars and libraries are increasingly using OCR-generated text for retrieval and analysis. However, the process of creating text through OCR introduces varying degrees of error to the text. The impact of these errors on natural language processing (NLP) tasks has only been partially studied. We perform a series of extrinsic assessment tasks — sentence segmentation, named entity recognition, dependency parsing, information retrieval, topic modelling and neural language model fine-tuning — using popular, out-of-the-box tools in order to quantify the impact of OCR quality on these tasks. We find a consistent impact resulting from OCR errors on our downstream tasks with some tasks more irredeemably harmed by OCR errors. Based on these results, we offer some preliminary guidelines for working with text produced through OCR.