We investigate diagnosability of stochastic discrete-event systems where the observation of certain events is unreliable, that is, there are non-zero probabilities of the misdetection and misclassification of events based on faulty sensor readings. Such sensor unreliability is unavoidable in applications such as nuclear energy generation. We propose the notions of uA- and uAA-diagnosability for stochastic automata and demonstrate their relationship with the concepts of A- and AA-diagnosabilty defined previously. We extend the concept of the stochastic diagnoser to the unreliable observation paradigm and find conditions for uA- and uAA-diagnosability.