In this work, we develop an automated, scalable, property-agnostic, and black-box protocol noncompliance checking framework called BLEDiff that can analyze and uncover noncompliant behavior in the Bluetooth Low Energy (BLE) protocol implementations. To overcome the enormous manual effort of extracting BLE protocol reference behavioral abstraction and security properties from a large and complex BLE specification, BLEDiff takes advantage of having access to multiple BLE devices and leverages the concept of differential testing to automatically identify deviant noncompliant behavior. In this regard, BLEDiff first automatically extracts the protocol FSM of a BLE implementation using the active automata learning approach. To improve the scalability of active automata learning for the large and complex BLE protocol, BLEDiff explores the idea of using a divide and conquer approach. BLEDiff essentially divides the BLE protocol into multiple sub-protocols, identifies their dependencies and extracts the FSM of each sub-protocol separately, and finally composes them to create the large protocol FSM. These FSMs are then pair-wise tested to automatically identify diverse deviations. We evaluate BLEDiff with 25 different commercial devices and demonstrate it can uncover 13 different deviant behaviors with 10 exploitable attacks.