We present an approach to automatic detection of Alzheimer's type dementia based on characteristics of spontaneous spoken language dialogue consisting of interviews recorded in natural settings. The proposed method employs additive logistic regression (a machine learning boosting method) on content-free features extracted from dialogical interaction to build a predictive model. The model training data consisted of 21 dialogues between patients with Alzheimer's and interviewers, and 17 dialogues between patients with other health conditions and interviewers. Features analysed included speech rate, turn-taking patterns and other speech parameters. Despite relying solely on content-free features, our method obtains overall accuracy of 86.5\%, a result comparable to those of state-of-the-art methods that employ more complex lexical, syntactic and semantic features. While further investigation is needed, the fact that we were able to obtain promising results using only features that can be easily extracted from spontaneous dialogues suggests the possibility of designing non-invasive and low-cost mental health monitoring tools for use at scale.