Alzheimer's disease (AD) is an increasingly prevalent cognitive disorder in which memory, language, and executive function deteriorate, usually in that order. There is a growing need to support individuals with AD and other forms of dementia in their daily lives, and our goal is to do so through speech-based interaction. Given that 33% of conversations with people with middle-stage AD involve a breakdown in communication, it is vital that automated dialogue systems be able to identify those breakdowns and, if possible, avoid them. In this article, we discuss several linguistic features that are verbal indicators of confusion in AD (including vocabulary richness, parse tree structures, and acoustic cues) and apply several machine learning algorithms to identify dialogue-relevant confusion from speech with up to 82% accuracy. We also learn dialogue strategies to avoid confusion in the first place, which is accomplished using a partially observable Markov decision process and which obtains accuracies (up to 96.1%) that are significantly higher than several baselines. This work represents a major step towards automated dialogue systems for individuals with dementia.