This paper performs a detailed, multi-faceted analysis of key challenges and common design caveats related to the development of efficient neural networks (NN) based nonlinear channel equalizers in coherent optical communication systems. The goal of this study is 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...