Automatic unreliable news detection is a research problem with great potential impact. Recently, several papers have shown promising results on large-scale news datasets with models that only use the article itself without resorting to any fact-checking mechanism or retrieving any supporting evidence. In this work, we take a closer look at these datasets. While they all provide valuable resources for future research, we observe a number of problems that may lead to results that do not generalize in more realistic settings. Specifically, we show that selection bias during data collection leads to undesired artifacts in the datasets. In addition, while most systems train and predict at the level of individual articles, overlapping article sources in the training and evaluation data can provide a strong confounding factor that models can exploit. In the presence of this confounding factor, the models can achieve good performance by directly memorizing the site-label mapping instead of modeling the real task of unreliable news detection. We observed a significant drop (>10%) in accuracy for all models tested in a clean split with no train/test source overlap. Using the observations and experimental results, we provide practical suggestions on how to create more reliable datasets for the unreliable news detection task. We suggest future dataset creation include a simple model as a difficulty/bias probe and future model development use a clean non-overlapping site and date split.