Depression and anxiety are psychiatric disorders that are observed in many areas of everyday life. For example, these disorders manifest themselves somewhat frequently in texts written by nondiagnosed users in social media. However, detecting users with these conditions is not a straightforward task as they may not explicitly talk about their mental state, and if they do, contextual cues such as immediacy must be taken into account. When available, linguistic flags pointing to probable anxiety or depression could be used by medical experts to write better guidelines and treatments. In this paper, we develop a dataset designed to foster research in depression and anxiety detection in Twitter, framing the detection task as a binary tweet classification problem. We then apply state-of-the-art classification models to this dataset, providing a competitive set of baselines alongside qualitative error analysis. Our results show that language models perform reasonably well, and better than more traditional baselines. Nonetheless, there is clear room for improvement, particularly with unbalanced training sets and in cases where seemingly obvious linguistic cues (keywords) are used counter-intuitively.