End-to-end multi-talker automatic speech recognition (MTASR) faces significant challenges in accurately transcribing overlapping speech. A critical bottleneck is that speaker-specific acoustic characteristics, which are essential for distinguishing overlapping speech, are often diluted in deep network layers. To address this, we propose the Global-Local Aware Dynamic Mixture-of-Experts (GLAD) architecture. GLAD introduces a novel routing mechanism that dynamically fuses speaker-aware global context with fine-grained local acoustic details to adaptively guide expert selection. Experiments on the LibriSpeechMix and CH109 datasets demonstrate that GLAD significantly outperforms existing Serialized Output Training (SOT)-based MTASR approaches, exhibiting exceptional robustness in challenging, high-overlap scenarios. To the best of our knowledge, this is the first work to apply a global-local fusion MoE strategy to MTASR.