Most agency pitches sound good. Slides are polished, case studies are impressive, and everyone in the room is likeable. None of that tells you what it's actually like to work together six months in, which is the only thing that matters.
The person pitching you is rarely the person doing the day-to-day work. Ask directly who will be on the account, how senior they are, and how much of their time is realistically split across other clients. A vague answer here is itself an answer.
Every agency relationship hits a point where the agency thinks you're wrong about something. How they've handled that in the past tells you more than any case study. Agencies that only ever say yes are agencies that will let a bad idea ship rather than risk the relationship.
Campaigns miss targets. That's normal. What matters is whether the agency has a real process for diagnosing why, or whether the answer is always "give it more time and more budget." Ask for a specific example of something that didn't work and what they changed because of it.
"Full-service" can mean twelve disciplines under one roof, or it can mean two generalists stretched across everything you need. Ask which services are handled by dedicated specialists versus generalists wearing multiple hats. Neither answer is automatically wrong, but you should know which one you're paying for.