Wikipedia is the largest online encyclopedia, used by algorithms and web users as a central hub of reliable information on the web. The quality and reliability of Wikipedia content is maintained by a community of volunteer editors. Machine learning and information retrieval algorithms could help scale up editors' manual efforts around Wikipedia content reliability. However, there is a lack of large-scale data to support the development of such research. To fill this gap, in this paper, we propose Wiki-Reliability, the first dataset of English Wikipedia articles annotated with a wide set of content reliability issues. To build this dataset, we rely on Wikipedia "templates". Templates are tags used by expert Wikipedia editors to indicate content issues, such as the presence of "non-neutral point of view" or "contradictory articles", and serve as a strong signal for detecting reliability issues in a revision. We select the 10 most popular reliability-related templates on Wikipedia, and propose an effective method to label almost 1M samples of Wikipedia article revisions as positive or negative with respect to each template. Each positive/negative example in the dataset comes with the full article text and 20 features from the revision's metadata. We provide an overview of the possible downstream tasks enabled by such data, and show that Wiki-Reliability can be used to train large-scale models for content reliability prediction. We release all data and code for public use.