Developers often leave behind clues in their code, admitting where it falls short, known as Self-Admitted Technical Debt (SATD). In the world of Scientific Software (SSW), where innovation moves fast and collaboration is key, such debt is not just common but deeply impactful. As research relies on accurate and reproducible results, accumulating SATD can threaten the very foundations of scientific discovery. Yet, despite its significance, the relationship between SATD and SSW remains largely unexplored, leaving a crucial gap in understanding how to manage SATD in this critical domain. This study explores SATD in SSW repositories, comparing SATD in scientific versus general-purpose open-source software and evaluating transformer-based models for SATD identification. We analyzed SATD in 27 scientific and general-purpose repositories across multiple domains and languages. We fine-tuned and compared 10 transformer-based models (100M-7B parameters) on 67,066 labeled code comments. SSW contains 9.25x more Scientific Debt and 4.93x more SATD than general-purpose software due to complex computations, domain constraints, and evolving research needs. Furthermore, our best model outperforms existing ones. This study uncovers how SATD in SSW differs from general software, revealing its impact on quality and scientific validity. By recognizing these challenges, developers and researchers can adopt smarter strategies to manage debt and safeguard the integrity of scientific discovery.