Many scientific studies deal with person counting and density estimation from single images. Recently, convolutional neural networks (CNNs) have been applied for these tasks. Even though often better results are reported, it is often not clear where the improvements are resulting from, and if the proposed approaches would generalize. Thus, the main goal of this paper was to identify the critical aspects of these tasks and to show how these limit state-of-the-art approaches. Based on these findings, we show how to mitigate these limitations. To this end, we implemented a CNN-based baseline approach, which we extended to deal with identified problems. These include the discovery of bias in the reference data sets, ambiguity in ground truth generation, and mismatching of evaluation metrics w.r.t. the training loss function. The experimental results show that our modifications allow for significantly outperforming the baseline in terms of the accuracy of person counts and density estimation. In this way, we get a deeper understanding of CNN-based person density estimation beyond the network architecture. Furthermore, our insights would allow to advance the field of person density estimation in general by highlighting current limitations in the evaluation protocols.