Although modern automatic speech recognition (ASR) systems can achieve high performance, they may produce errors that weaken readers' experience and do harm to downstream tasks. To improve the accuracy and reliability of ASR hypotheses, we propose a cross-modal post-processing system for speech recognizers, which 1) fuses acoustic features and textual features from different modalities, 2) joints a confidence estimator and an error corrector in multi-task learning fashion and 3) unifies error correction and utterance rejection modules. Compared with single-modal or single-task models, our proposed system is proved to be more effective and efficient. Experiment result shows that our post-processing system leads to more than 10% relative reduction of character error rate (CER) for both single-speaker and multi-speaker speech on our industrial ASR system, with about 1.7ms latency for each token, which ensures that extra latency introduced by post-processing is acceptable in streaming speech recognition.