Dementia is associated with language disorders which impede communication. Here, we automatically learn linguistic disorder patterns by making use of a moderately-sized pre-trained language model and forcing it to focus on reformulated natural language processing (NLP) tasks and associated linguistic patterns. Our experiments show that NLP tasks that encapsulate contextual information and enhance the gradient signal with linguistic patterns benefit performance. We then use the probability estimates from the best model to construct digital linguistic markers measuring the overall quality in communication and the intensity of a variety of language disorders. We investigate how the digital markers characterize dementia speech from a longitudinal perspective. We find that our proposed communication marker is able to robustly and reliably characterize the language of people with dementia, outperforming existing linguistic approaches; and shows external validity via significant correlation with clinical markers of behaviour. Finally, our proposed linguistic disorder markers provide useful insights into gradual language impairment associated with disease progression.