LLM-empowered paper-code discrepancy detection has received growing concern since the scaling of research submissions exceeds the manual review capability. However, the limited context capacity and one-sided discrepancy detection of existing single-agent LLM paradigms lead to an inferior recall performance in detecting discrepancies. In this paper, we propose **Dude**, the first **Du**al-**De**tection Multi-Agent System for paper-code discrepancy detection. We discover that the granularity asymmetry of the paper-language and code-language introduces over-interpretation and over-reporting challenges in a multi-agent system design for discrepancy detection, resulting in increasing false positives. To address this, we propose a granularity-aligned negotiation and a two-stage salience-filtering mechanism in Dude, which effectively prevents agents from falsely reporting discrepancies. Experimental results in real-world paper-code discrepancy datasets showcase Dude’s significant recall and precision improvement by up to **22.8%**, increasing F1 score by up to **18.7%** compared to baseline methods.