Here are a few very simple things to do if you are determined to buy online advertising.
Buy directly from quality publishers or quality publisher networks.
Stay away from open ad networks and programmatic buying.
Do not trust any reports you get from your agency. It's not that the agencies are corrupt, it's just that they get their data mostly from their suppliers, who are unreliable.
Do not rely on reports from the major fraud detection or ad verification suppliers. They have been shown to be unreliable.
Do not rely on "seals of approval" from organizations that supposedly vet websites.
Question everything about a proposed media buy. The most important question to ask is: "How do you know this?"
If you spend substantially on online advertising, work with a trusted consultant. I am not in the habit of making recommendations on suppliers, but if you've read this book you know who I trust and who I don't.