The Agile community has some good ideas to pass down to conventional project managers, including:
While it may not be possible to iterate the building of a piece of machinery, engaging and explaining to the customer in their language--no jargon--what's happening will highlight issues early. If the customer doesn't like something, the sooner you know, the better.
One of the key tenets of Agile is to engage effectively with your customer and end-users, understand their needs and problems, and then deliver an effective solution. This requires regular and effective communication, openness and accountability, and a good measure of trust to support robust relationships between the project team and their key stakeholders. It's a pity so many project managers put their energies into fighting the client rather than collaborating.
Going Light and Lean
Those are hardly new ideas, but they've been embraced by the Agile philosophy for a good reason: They work. Lean was developed by Toyota as a manufacturing philosophy and has been adapted to many other areas. Some of its key principles--such as minimizing unnecessary movement, simplifying process and continuous improvement--have huge potential in project management.
Light is focused on the minimizing unnecessary overhead. Complex plans and processes should be simplified, but only to remove excess complication, not to remove core requirements.
Slimming down the project management overhead to its optimal level is probably the easiest way to free up the resources needed to engage your stakeholders more effectively and is definitely supported by the A Guide to the Project Management Body of Knowledge (PMBOK® Guide).
For more information, see Light Versus Lean -- Steps to Improve Project Efficiency from PMI's Community Post.