Recent advances in text classification and knowledge capture in language models have relied on availability of large-scale text datasets. However, language models are trained on static snapshots of knowledge and are limited when that knowledge evolves. This is especially critical for misinformation detection, where new types of misinformation continuously appear, replacing old campaigns. We propose time-aware misinformation datasets to capture time-critical phenomena. In this paper, we first present evidence of evolving misinformation and show that incorporating even simple time-awareness significantly improves classifier accuracy. Second, we present COVID-TAD, a large-scale COVID-19 misinformation da-taset spanning 25 months. It is the first large-scale misinformation dataset that contains multiple snapshots of a datastream and is orders of magnitude bigger than related misinformation datasets. We describe the collection and labeling pro-cess, as well as preliminary experiments.