Automatic detection of sleepiness can help to improve the follow-up of patients suffering from chronic diseases. Previous research on sleepiness detection has shown that this task is feasible using voice recordings. Most studies however rely on numerous features extracted from healthy subjects recordings and machine learning, the target being the output of subjective sleepiness questionnaires. In this paper, we propose to study the reading errors made by patients suffering from Excessive Daytime Sleepiness on the MSLT database collected at the Bordeaux hospital. This database differs from the others on two key points: patients are recorded instead of healthy subjects and their sleepiness level is assessed using multiple measurements, both subjective and objective. With the help of Speech Therapists, we defined and counted reading errors and confront these numbers with sleepiness measurements. We show that evaluating these reading errors can be useful to elaborate robust markers of objective sleepiness but also to elaborate exclusion criteria of the speakers not having a sufficient reading level.