The Mini Mental State Examination (MMSE) is a standardized cognitive health screening test. It is generally administered by trained clinicians, which may be time-consuming and costly. An intriguing and scalable alternative is to detect changes in cognitive function by automatically monitoring individuals’ memory and language abilities from their conversational narratives. We work towards doing so by predicting clinical MMSE scores using verbal and non-verbal features extracted from the transcripts of 108 speech samples from the ADReSS Challenge dataset. We achieve a Root Mean Squared Error (RMSE) of 4.34, a percentage decrease of 29.3% over the existing performance benchmark. We also explore the performance impacts of acoustic versus linguistic, text-based features and find that linguistic features achieve lower RMSE scores, providing strong positive support for their inclusion in future MMSE score prediction models. Our best-performing model leverages a selection of verbal and non-verbal cues, demonstrating that MMSE score prediction is a rich problem that is best addressed using input from multiple perspectives.