The problems that come from having the wrong people do your strategic planning are sometimes harder to spot. A plan that has glaring omissions of data or perspective, a plan with poor management team support, and a plan that looks like the CEO wrote it by himself (or herself) are all examples of a plan that may have been created by the wrong people.
So - who should do your strategic planning? Ideally, the strategic planning process should be undertaken by a strategic planning team made up of the CEO and his or her direct reports. In a perfect world, this would be a team of 6-8 people who have intimate knowledge of all the different facets of your business - markets, operations, and financial issues. This group must also have the ability to implement the plan through their day-to-day involvement with the operation of your business. This means that the primary strategic decision making role should go to the people with the primary strategy implementation responsibilities. NOT the board of directors, NOT outside suppliers or union representatives, NOT customer representatives, and NOT a consultant. There are roles for all of these people in your planning process, but the decisions need to be made by the people who will actually have to carry them out. A really good strategic planning consultant, for example, will coach your team through the process in a way that saves them time and stimulates them to better strategic thinking. But by no means should such an outside actually set your strategic for you!
The key idea here is that there are two critical things required for a good plan to work: one is input from the right people, and the other is commitment from the right people. Involving the right people in your strategic planning process will get you both.