Automatic Video Dubbing (AVD) generates speech aligned with lip motion and facial emotion from scripts. Recent research focuses on modeling multimodal context to enhance prosody expressiveness but overlooks two key issues: 1) Multiscale prosody expression attributes in the context influence the current sentence's prosody. 2) Prosody cues in context interact with the current sentence, impacting the final prosody expressiveness. To tackle these challenges, we propose M2CI-Dubber, a Multiscale Multimodal Context Interaction scheme for AVD. This scheme includes two shared M2CI encoders to model the multiscale multimodal context and facilitate its deep interaction with the current sentence. By extracting global and local features for each modality in the context, utilizing attention-based mechanisms for aggregation and interaction, and employing an interaction-based graph attention network for fusion, the proposed approach enhances the prosody expressiveness of synthesized speech for the current sentence. Experiments on the Chem dataset show our model outperforms baselines in dubbing expressiveness. The code and demos are available at \textcolor[rgb]{0.93,0.0,0.47}{https://github.com/AI-S2-Lab/M2CI-Dubber}.