An autoencoder is trained by replicating each training instance to both input and output. However, when predicting for anomaly detection, will the output error be local to the same output feature(s) that were anomalous inputs e.g. if I have 10 features, and I predict with anomalous input on feature #4, will the high output error be limited to output feature #4 as well, or will high error appear on other outputs? The whole detection becomes more useful if localised to specific features.
The output error will be propagated to the subsequent layers, so if your auto-encoder learns a function over all the features, the anomaly will be weaved across all the features you used as input. One trick is to map specific features (or set of features) to different auto-encoders, and train them as an ensemble. Whether you desire to integrate the specific features anomaly in a global outlier score, or maintain outlier scores for subset of features is then a design choice. For a good use case, see this recent paper.
Experimentation has shown that there is some localisation between input and output, however that locality decreases as the number of layers increases. Presumably, with each additional layer, the reconstruction becomes less localised as the error is shared amongst all the outputs from a neuron at that layer, and hence the error spreads with each successive output layer. The end result is that in an image, reconstruction pixel error is localised around each input pixel, but the more layers, the wider the spread of error is located around the input pixel in question