Claire,
Everything that you mentioned above can and should be handled in the Project Meeting.
Spelling out the requirements, getting those requirements in writing, with milestones, that have both penalties and rewards for being ahead of schedule and behind schedule, and a Change Order process that clearly defines how scope creep can and will be handled in the event that the requirements change. All of this needs to be clearly defined in the Project Kick Off meeting.
A good project manager, is as important as a good developer, and in some cases more important. The Project Manager not only handles the timeline of the project and the requirements, but also manages the customer. Most people forget that, a good project manager has a unique skill set.
So I must disagree, if the project is handled correctly, and there is a good communication chain between the project team and the customer, issues that arrive during the development, and they will, can be effectively handled.