Alzheimer's Disease (AD) is associated with many characteristic changes, not only in an individual's language but also in the interactive patterns observed in dialogue. The most indicative changes of this latter kind tend to be associated with relatively rare dialogue acts (DAs), such as those involved in clarification exchanges and responses to particular kinds of questions. However, most existing work in DA tagging focuses on improving average performance, effectively prioritizing more frequent classes; it thus gives a poor performance on these rarer classes and is not suited for application to AD analysis. In this paper, we investigate tagging specifically for rare class DAs, using a hierarchical BiLSTM model with various ways of incorporating information from previous utterances and DA tags in context. We show that this can give good performance for rare DA classes on both the general Switchboard corpus (SwDA) and an AD-specific conversational dataset, the Carolinas Conversation Collection (CCC); and that the tagger outputs then contribute useful information for distinguishing patients with and without AD