Early involvement via sprint demosAgile advocates that stakeholders (or proxies in the form of product owners) be part of the team. This is an admirable goal, but I've yet to see it occur in practice. This may be due to my experience in product development companies, where the "customer" is a market, not specific people. While I've not had the opportunity to embed customers in my teams, there are ways to integrate them in your process.
Make each product owner responsible for cultivating a cadre of users. These users are people heavily involved in the operational workflows for which the product is intended to be used. Beginning with the first storyboards, this collection of users participates in sprint demonstrations. They are made aware of the user stories delivered and the user stories being considered for the next iteration. As the product is demonstrated, they can immediately confirm or correct workflow and visual designs. I've even witnessed users helping each other understand how to use the product, thereby eliminating feature requests entirely.
This group also is a sounding board for questions or ideas that come up during the development process. It is not unusual for product owners to have multiple user contacts through an iteration.
Advisory boardsWhile iteration demonstrations are tactical, advisory boards are strategic. Look for people with industry breadth and understanding of operations within their organizations. Advisory boards are critical to ensuring appropriate major product features and workflows. Instead of focusing on iteration deliverables, this group guides you to determine priorities of competing major features, high level workflows across features, and your standing relative to competitors (within ethical and legal constraints).
You will want 8-12 people representing multiple dimensions of your product. For example, a product for physicians would have an advisory board comprised of multiple specialties, geographies, and EHR usage. I encourage you to have non-customers represented, as well. They are highly likely to provide you completely new ways of thinking about problems, since they don't "know" your product or its workflows.
Most importantly, you want this group to tell you where your strategic mistakes are - before the market does.
These two groups can tremendously impact your ability to deliver a highly acceptable product to the market. They help refine workflows and visual designs, thereby decreasing the time to customer satisfaction. Equally important, the people involved throughout take a high degree of ownership. They become product advocates, since it is their product design.