This work investigates a practical reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) system, where a subset of RIS elements fail to function properly and reflect incident signals randomly towards unintended directions with attenuation, thereby degrading system performance. To date, no study has addressed such impairments caused by faulty RIS elements in ISAC systems. This work aims to fill the gap. First, to quantify the impact of faulty elements on ISAC performance, we derive the misspecified Cramér-Rao bound (MCRB) for sensing parameter estimation and signal-to-interference-and-noise ratio (SINR) for communication quality. Then, to mitigate the performance loss caused by faulty elements, we jointly design the remaining functional RIS phase shifts and transmit beamforming to minimize the MCRB, subject to the communication SINR and transmit power constraints. The resulting optimization problem is highly non-convex due to the intricate structure of the MCRB expression and constant-modulus constraint imposed on RIS. To address this, we reformulate it into a more tractable form and propose a block coordinate descent (BCD) algorithm that incorporates majorization-minimization (MM), successive convex approximation (SCA), and penalization techniques. Simulation results demonstrate that our proposed approach reduces the performance loss by 21.25% on average compared to the baseline where the presence of faulty elements is ignored. Furthermore, the performance gain becomes more evident as the number of faulty elements increases.