Quality management when creating large-scale speech datasets is essential for building reliable downstream models, yet verification pipelines are often brittle, domain-specific, and expertise-intensive. We introduce **SpeechQM-Agent**, a natural language-driven agentic framework that compiles user requirements into dependency-aware DAG workflows over modular tools for audio, transcript, and metadata verification. A central planner LLM enforces prerequisites and supports execution-time replanning (e.g., re-running failed steps or swapping tools), reducing manual pipeline engineering and improving robustness across heterogeneous vendor formats and multilingual settings. We also release **SpeechQM-Dataset**, a multilingual benchmark with controlled, vendor-inspired quality artifacts spanning 24 verification tasks. Across experiments, SpeechQM-Agent attains **80-90%** agreement with expert verification while requiring **<20%** of the cost and time of manual QC, and we further validate transfer to real vendor-supplied corpora. Planner LLM comparisons highlight fidelity-efficiency trade-offs.