The prevalent approach in speech emotion recognition (SER) involves integrating both audio and textual information to comprehensively identify the speaker's emotion, with the text generally obtained through automatic speech recognition (ASR). An essential issue of this approach is that ASR errors from the text modality can worsen the performance of SER. Previous studies have proposed using an auxiliary ASR error detection task to adaptively assign weights of each word in ASR hypotheses. However, this approach has limited improvement potential because it does not address the coherence of semantic information in the text. Additionally, the inherent heterogeneity of different modalities leads to distribution gaps between their representations, making their fusion challenging. Therefore, in this paper, we incorporate two auxiliary tasks, ASR error detection (AED) and ASR error correction (AEC), to enhance the semantic coherence of ASR text, and further introduce a novel multi-modal fusion (MF) method to learn shared representations across modalities. We refer to our method as MF-AED-AEC. Experimental results indicate that MF-AED-AEC significantly outperforms the baseline model by a margin of 4.1\%.