We propose a Perceiver-based sequence classifier to detect abnormalities in speech reflective of several neurological disorders. We combine this classifier with a Universal Speech Model (USM) that is trained (unsupervised) on 12 million hours of diverse audio recordings. Our model compresses long sequences into a small set of class-specific latent representations and a factorized projection is used to predict different attributes of the disordered input speech. The benefit of our approach is that it allows us to model different regions of the input for different classes and is at the same time data efficient. We evaluated the proposed model extensively on a curated corpus from the Mayo Clinic. Our model outperforms standard transformer (80.9%) and perceiver (81.8%) models and achieves an average accuracy of 83.1%. With limited task-specific data, we find that pretraining is important and surprisingly pretraining with the unrelated automatic speech recognition (ASR) task is also beneficial. Encodings from the middle layers provide a mix of both acoustic and phonetic information and achieve best prediction results compared to just using the final layer encodings (83.1% vs. 79.6%). The results are promising and with further refinements may help clinicians detect speech abnormalities without needing access to highly specialized speech-language pathologists.