Large language models (LLMs) are frequently fine-tuned or unlearned to adapt to new tasks or eliminate undesirable behaviors. While existing evaluation methods assess performance after such interventions, there remains no general approach for detecting unintended side effects—such as unlearning biology content degrading performance on chemistry tasks, particularly when these effects are unpredictable or emergent. To address this issue, we introduce MNEME, textitModel diffiNg for Evaluating Mechanistic Effects, a lightweight framework for identifying these side effects using sparse model diffing. MNEME compares base and fine-tuned models on task-agnostic data (e.g., The Pile, LMSYS-Chat-1M), without access to fine-tuning data, to isolate behavioral shifts. Applied to five LLMs across three scenarios, WMDP knowledge unlearning, emergent misalignment, and benign fine-tuning—MNEME achieves up to 95\% accuracy in predicting side effects, aligning with known benchmarks and requiring no custom heuristics. Furthermore, we show that retraining on high-activation samples can partially reverse these effects. Our results demonstrate that sparse probing and diffing offer a scalable and automated lens into fine-tuning-induced model changes, providing practical tools for understanding and managing LLM behavior.