Paper weakness identification using single-agent or multi-agent LLMs has attracted increasing attention, yet existing approaches exhibit key limitations. Many multi-agent systems simulate human roles at a surface level, missing the underlying criteria that lead experts to assess complementary intellectual aspects of a paper. Moreover, prior methods implicitly assume identified weaknesses are valid, ignoring reviewer bias, misunderstanding, and the critical role of author rebuttals in validating review quality. Finally, most systems output unranked weakness lists, rather than prioritizing the most consequential issues for users. In this work, we propose DIAGPaper, a novel multi-agent framework that addresses these challenges through three tightly integrated modules. The customizer module simulates human-defined review criteria and instantiates multiple reviewer agents with criterion-specific expertise. The rebuttal module introduces author agents that engage in structured debate with reviewer agents to validate and refine proposed weaknesses. The prioritizer module learns from large-scale human review practices to assess the severity of validated weaknesses and surfaces the top-K severest ones to users. Experiments on two benchmarks, AAAR and ReviewCritique, demonstrate that DIAGPaper substantially outperforms existing methods by producing more valid and more paper-specific weaknesses, while presenting them in a user-oriented, prioritized manner.