In a shul with which I am familiar, the established custom has long been that the Rabbi gives a d'var torah before Shabbat Musaf. On the rare occasions when the Rabbi is out of town, he will invite a congregant or a visiting scholar to give a d'var torah in his stead. If the invited speaker is a man, he speaks at the usual point in the service (before Musaf). However, if the invited speaker is a woman, she instead speaks at the end of Musaf, right before Adon Olam.
Based on this established practice, I infer that there are some halachic issues with having a woman speak to the congregation specifically at that point in the service -- issues that are obviated by having her speak after the service is over. What might those issues be?