Multimodal Large Language Models (MLLMs) hold significant promise for revolutionizing traditional education and reducing teachers' workload. However, accurately interpreting unconstrained STEM student handwritten solutions with intertwined mathematical formulas, diagrams, and textual reasoning poses a significant challenge due to the lack of authentic and domain-specific benchmarks. Additionally, current evaluation paradigms predominantly rely on the outcomes of downstream tasks (e.g., auto-grading), which often probe only a subset of the recognized content, thereby failing to capture the MLLMs' understanding of complex handwritten logic as a whole. To bridge this gap, we release EDU-CIRCUIT-HW, a dataset consisting of 1,300+ authentic student handwritten solutions from a university-level STEM course. Utilizing the expert-verified verbatim transcriptions and grading reports of student solutions, we simultaneously evaluate various MLLMs' upstream recognition fidelity and downstream auto-grading performance. Our evaluation uncovers an astonishing scale of latent failures within MLLM-recognized student handwritten content, highlighting the models' insufficient reliability for auto-grading and other understanding-oriented applications in high-stakes educational settings. As a potential solution, we present a case study demonstrating that leveraging identified error patterns to preemptively detect and correct recognition errors, while requiring only minimal human intervention (e.g., routing 3.3% of assignments to human graders and the remainder to the GPT-5.1 grader), can effectively enhance the robustness of the deployed AI-enabled grading system. Code and dataset are available in this GitHub repo: https://gt-learning-innovation.github.io/CIRCUIT_EDU_HW_ACL.