This paper addresses the problem of fault detection (FD) for discrete-time networked systems with global Lipschitz conditions and imperfect measurements. By using Bernoulli stochastic variables and a switching signal, a unified model is proposed to describe four kinds of imperfect measurements, that is, access constraints, time delays, packet dropouts, and signal quantization. We aim to design a fault detection filter (FDF) such that, for all external disturbances and imperfect measurements, the error between the residual and fault is made as small as possible. The addressed FD problem is then converted into an auxiliary $H_{infty}$ filtering problem for discrete-time stochastic switched systems with multiple time-varying delays. By applying Lyapunov-Krasovskii approach, a sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the results obtained.