Speech translation (ST) is an enabling technology for cross-lingual oral communication. A ST system consists of two major components: an automatic speech recognizer (ASR) and a machine translator (MT). Nowadays, most ASR systems are trained and tuned by minimizing word error rate (WER). However, WER counts word errors at the surface level. It does not consider the contextual and syntactic roles of a word, which are often critical for MT. In the end-to-end ST scenarios, whether WER is a good metric for the ASR component of the full ST system is an open issue and lacks systematic studies. In this paper, we report our recent investigation on this issue, focusing on the interactions of ASR and MT in a ST system. We show that BLEU-oriented global optimization of ASR system parameters improves the translation quality by an absolute 1.5% BLEU score, while sacrificing WER over the conventional, WER-optimized ASR system. We also conducted an in-depth study on the impact of ASR errors on the final ST output. Our findings suggest that the speech recognizer component of the full ST system should be optimized by translation metrics instead of the traditional WER.