A widely used approach for neural machine translation (NMT) is to train an autoregressive model by maximizing the probability of training sentence pairs in conjunction with a mode-seeking decoding strategy for inference. The ultimate goal is to reduce the system error, i.e. to achieve a high translation quality of unseen sentences. However, this high-level perspective is oblivious to potential pitfalls within the training and decoding pipeline. In this work we propose to measure mode and search errors in addition to the system error in order to better understand the connections amongst them. We study how these errors change when we vary both the decoding strategy and the degree of sparsity of the learned distribution. First, we empirically confirm the high prevalence of modeling errors in NMT, and that the relation between search error and system error is highly non-monotonic. Second, we show that adding sparsity to the model can effectively reduce both mode and search error. Analyzing the mode translations shows that the qualitative improvements are partially due to better length modeling. However, the overall system error slowly increases as we make the decoder sparse suggesting that the current choice of decoding strategy can be further improved in the context of sparse models.