Despite recent progress in solving the state estimation problem, its real-time performance remains challenged by the presence of bad data, increasing computational demands for detection and identification. A state estimator uses neighboring measurements to estimate the system states, similar to how a graph neural network (GNN) refines node embeddings (bus states) based on messages from neighboring nodes. This paper proposes a GNN-based framework that detects and identifies bad data before providing measurements to the state estimator. The framework incorporates grid topology, employs node and edge features, and exploits correlations of measurement data to enhance identification accuracy. Specifically, an edge-conditioned GNN is developed to transform graph-based features into categories that detect bad measurements and identify their sources. The generated dataset uses historical load profiles and includes conventional and synchrophasor measurements to emulate real-life applications. The proposed framework is tested on MATPOWER 6-bus and IEEE 14-, 30-, 118-, and 300-bus systems. The results demonstrate high accuracy and illustrate graph-learning patterns. Thus, operators can take preventive actions before the bad measurements propagate through the state estimator.