Despite the rapid advancements in consumer electronics, the data transmitted by sensing devices in a smart home environment are still vulnerable to anomalies due to node faults, transmission errors, or attacks. This affects the reliability of the received sensed data and may lead to the incorrect decision making at both local (i.e., smart home) and global (i.e., smart city) levels. This study introduces a novel mobile agent-based cross-layer anomaly detection scheme, which takes into account stochastic variability in cross-layer data obtained from received data packets, and defines fuzzy logic-based soft boundaries to characterize behavior of sensor nodes. This cross-layer design approach empowers the proposed scheme to detect both node and link anomalies, and also effectively transmits mobile agents by considering the communication link-state before transmission of the mobile agent. The proposed scheme is implemented on a real testbed and a modular application software is developed to manage the anomaly detection system in the smart home. The experimental results show that the proposed scheme detects cross-layer anomalies with high accuracy and considerably reduces the energy consumption caused by the mobile agent transmission in the poor communication link-state situations.