Large language models (LLMs) show increasing promise in medical applications, but their ability to detect and correct errors in clinical texts—a prerequisite for safe deployment—remains under-evaluated, particularly beyond English. We introduce MEDRECT, a cross-lingual benchmark (Japanese/English) that formulates medical error handling as three subtasks: error detection, error localization (sentence extraction), and error correction. MEDRECT is built with a scalable, automated pipeline from the Japanese Medical Licensing Examinations (JMLE) and a curated English counterpart, yielding MEDRECT-ja (663 texts) and MEDRECT-en (458 texts) with comparable error/no-error balance. We evaluate 9 contemporary LLMs spanning proprietary, open-weight, and reasoning families. Key findings: (i) reasoning models substantially outperform standard architectures, with up to 13.5% relative improvement in error detection and 51.0% in sentence extraction; (ii) cross-lingual evaluation reveals 5-10% performance gaps from English to Japanese, with smaller disparities for reasoning models; (iii) targeted LoRA fine-tuning yields asymmetric improvements in error correction performance (Japanese: +0.078, English: +0.168) while preserving reasoning capabilities; and (iv) our fine-tuned model exceeds human expert performance on structured medical error correction tasks. To our knowledge, MEDRECT is the first comprehensive cross-lingual benchmark for medical error correction, providing a reproducible framework and resources for developing safer medical LLMs across languages.