Autoencoders are widely used in machine learning applications, in particular for anomaly detection. Hence, they have been introduced in high energy physics as a promising tool for model-independent new physics searches. We scrutinize the usage of autoencoders for unsupervised anomaly detection based on reconstruction loss to show their capabilities, but also their limitations. As a particle physics benchmark scenario, we study the tagging of top jet images in a background of QCD jet images. Although we reproduce the positive results from the literature, we show that the standard autoencoder setup cannot be considered as a model-independent anomaly tagger by inverting the task: due to the sparsity and the specific structure of the jet images, the autoencoder fails to tag QCD jets if it is trained on top jets even in a semi-supervised setup. Since the same autoencoder architecture can be a good tagger for a specific example of an anomaly and a bad tagger for a different example, we suggest improved performance measures for the task of model-independent anomaly detection. We also improve the capability of the autoencoder to learn non-trivial features of the jet images, such that it is able to achieve both top jet tagging and the inverse task of QCD jet tagging with the same setup. However, we want to stress that a truly model-independent and powerful autoencoder-based unsupervised jet tagger still needs to be developed.