In critical Internet of Things (IoT) application domains, such as the Defense Industry and Healthcare, false alerts have many negative effects, such as fear, disruption of emergency services, and waste of resources. Therefore, an alert must only be sent if triggered by a correct event. Nevertheless, IoT networks are exposed to intrusions, which affects event detection accuracy. In this paper, an Anomaly Detection System (ADS) is proposed in a smart hospital IoT system for detecting events of interest about patients' health and environment and, at the same time, for network intrusions. Providing a single system for network infrastructure supervision and e-health monitoring has been shown to optimize resources and enforce the system reliability. Consequently, decisions regarding patients' care and their environments' adaptation are more accurate. The low latency is ensured, thanks to a deployment on the edge to allow for a processing close to data sources. The proposed ADS is implemented and evaluated while using Contiki Cooja simulator and the e-health event detection is based on a realistic data-set analysis. The results show a high detection accuracy for both e-health related events and IoT network intrusions.