  This paper performs a detailed, multi-faceted analysis of key challenges and
common design caveats related to the development of efficient neural networks
(NN) nonlinear channel equalizers in coherent optical communication systems.
Our study aims to guide researchers and engineers working in this field. We
start by clarifying the metrics used to evaluate the equalizers' performance,
relating them to the loss functions employed in the training of the NN
equalizers. The relationships between the channel propagation model's accuracy
and the performance of the equalizers are addressed and quantified. Next, we
assess the impact of the order of the pseudo-random bit sequence used to
generate the -- numerical and experimental -- data as well as of the DAC memory
limitations on the operation of the NN equalizers both during the training and
validation phases. Finally, we examine the critical issues of overfitting
limitations, the difference between using classification instead of regression,
and batch-size-related peculiarities. We conclude by providing analytical
expressions for the equalizers' complexity evaluation in the digital signal
processing (DSP) terms and relate the metrics to the processing latency.
