Machine translation systems still make systematic errors on idioms and other expressions that cannot be translated literally. Model editing offers a possible way to fix such recurring errors without retraining the whole model, but it has mostly been studied for monolingual factual updates rather than translation. We introduce MEMT-bench, the first benchmark for evaluating model editing in machine translation across multiple languages, models, and editing settings. The benchmark is built from idiomatic translation errors and tests whether an edit can correct a targeted mistranslation while preserving unrelated translation behavior. Experiments with causal tracing and representative editing methods reveal both the promise and difficulty of translation editing: edits can repair targeted errors, but maintaining cross-lingual locality and robustness under repeated edits remains challenging. Code and data are publicly available at [GitHub](https://github.com/dannalily/MEMT-Model-Editing-for-Targeted-Translation-Error-Repair/) and [Hugging Face](https://huggingface.co/datasets/Dannalily/MEMT-bench), respectively.

Large language models (LLMs) have shown great potential in natural language processing tasks, but their application to machine translation (MT) remains challenging due to pretraining on English-centric data and the complexity of reinforcement learning from human feedback (RLHF). Direct Preference Optimization (DPO) has emerged as a simpler and more efficient alternative, but its performance depends heavily on the quality of preference data. To address this, we propose Confidence-Reward driven Preference Optimization (CRPO), a novel method that combines reward scores with model confidence to improve data selection for fine-tuning. CRPO selects challenging sentence pairs where the model is uncertain or underperforms, leading to more effective learning. While primarily designed for LLMs, CRPO also generalizes to encoder-decoder models like NLLB, demonstrating its versatility. Empirical results show that CRPO outperforms existing methods such as RS-DPO, RSO and MBR score in both translation accuracy and data efficiency.