Software engineering techniques are increasingly relying on deep learning approaches to support many software engineering tasks, from bug triaging to code generation. To assess the efficacy of such techniques researchers typically perform controlled experiments. Conducting these experiments, however, is particularly challenging given the complexity of the space of variables involved, from specialized and intricate architectures and algorithms to a large number of training hyper-parameters and choices of evolving datasets, all compounded by how rapidly the machine learning technology is advancing, and the inherent sources of randomness in the training process. In this work we conduct a mapping study, examining 194 experiments with techniques that rely on deep neural networks appearing in 55 papers published in premier software engineering venues to provide a characterization of the state-of-the-practice, pinpointing experiments common trends and pitfalls. Our study reveals that most of the experiments, including those that have received ACM artifact badges, have fundamental limitations that raise doubts about the reliability of their findings. More specifically, we find: 1) weak analyses to determine that there is a true relationship between independent and dependent variables (87% of the experiments), 2) limited control over the space of DNN relevant variables, which can render a relationship between dependent variables and treatments that may not be causal but rather correlational (100% of the experiments), and 3) lack of specificity in terms of what are the DNN variables and their values utilized in the experiments (86% of the experiments) to define the treatments being applied, which makes it unclear whether the techniques designed are the ones being assessed, or how the sources of extraneous variation are controlled. We provide some practical recommendations to address these limitations.