STM32F401RE Nucleo failing to read DHT22 sensor
In cases like these keep the following points in mind:


Haven't used on MBED but use a debugging tool like OpenOCD bundled with gdb and try to debug the code while looking at the input registers. In eclipse you can do it with a tool like EmbSysRegisters. Google for some tutorials and you'll save a lot of time.
Looking at the datasheet of DHT22, it says it needs a MCU to sensor signal to initiate the process. Have you checked that?