Welcome to the platform. The single most important thing to internalize early: Discovery and Service Mapping are only as good as your identification rules and your CSDM alignment. Get those wrong and you'll spend months chasing duplicates and broken maps.

On your five questions:

1. Running Discovery — nail MID Server placement and credential affinities first, scope schedules by IP range for horizontal (infra) Discovery, and work the ECC queue and Discovery logs to zero out errors before you trust anything.
2. Accuracy — this is the Identification & Reconciliation Engine. Confirm your CI Identifiers are correct so records update instead of duplicating, schedule Discovery regularly, and use "last discovered" to catch staleness.
3. Service Mapping validation — verify entry points, review each map for missing or wrong connections, use traffic-based/suggested connections, and confirm services roll up correctly to CSDM (Application Service → business/technical service).
4. Pitfalls — loading CIs without identification rules, skipping CSDM, ignoring Discovery errors, and having no named data-governance owner.
5. Health — the CMDB Health dashboards (Completeness, Correctness, Compliance) plus Data Manager and certification are your scorecard; trend the KPIs and assign remediation owners.

Frankly, most "is Discovery working right?" struggles aren't a tooling problem — they're a skills and process gap. Agree your identifiers, CSDM model, and governance owner up front and the metrics follow.

If you want a structured way to stand this up, we do exactly this at Four Dragons: