Rate-splitting multiple access (RSMA) is a general and powerful multiple access technique for downlink multi-antenna systems due to its robustness against imperfect channel knowledge. Most previous studies consider imperfect channel state information (CSI) at the transmitter (CSIT) only, which is not a practical assumption. Motivated by this issue, this paper aims to address the weighted sum-rate (WSR) maximization problem of RSMA under imperfect CSI at the receiver (CSIR) as well as CSIT. To this end, we put forth a novel precoder design framework when both channel estimation and channel feedback errors exist. Due to the feedback errors, the transmitter does not know the exact achievable rate at the receiver by Shannons capacity formula. Thus, we alternatively use an information-theoretic tool of generalized mutual information (GMI) in order to quantify the achievable rate with respect to the CSI errors. For solving the WSR optimization problem, which is non-convex, we propose a novel algorithm based on a convex-concave procedure (CCP). Numerical results show that RSMA is a quite robust transmission scheme in the absence of perfect CSIT and CSIR for multi-antenna systems.