As a new neural machine translation approach, NonAutoregressive machine Translation (NAT) has attracted attention recently due to its high efficiency in inference. However, the high efficiency has come at the cost of not capturing the sequential dependency on the target side of translation, which causes NAT to suffer from two kinds of translation errors: 1) repeated translations (due to indistinguishable adjacent decoder hidden states), and 2) incomplete translations (due to incomplete transfer of source side information via the decoder hidden states). In this paper, we propose to address these two problems by improving the quality of decoder hidden representations via two auxiliary regularization terms in the training process of an NAT model. First, to make the hidden states more distinguishable, we regularize the similarity between consecutive hidden states based on the corresponding target tokens. Second, to force the hidden states to contain all the information in the source sentence, we leverage the dual nature of translation tasks (e.g., English to German and German to English) and minimize a backward reconstruction error to ensure that the hidden states of the NAT decoder are able to recover the source side sentence. Extensive experiments conducted on several benchmark datasets show that both regularization strategies are effective and can alleviate the issues of repeated translations and incomplete translations in NAT models. The accuracy of NAT models is therefore improved significantly over the state-of-the-art NAT models with even better efficiency for inference.