I've been told that Montessori is "unstructured".

Is this is true?
How do the children learn in such an environment?
How does a teacher know that every child is learning if every child isn't doing the exact thing at the exact same time?

There is a lot of structure in a Montessori classroom!  It's just a different type of structure than in the traditional classroom. In many traditional classrooms since all the children do pretty much the same thing at the same time, the "structure" is in keeping them focused and quiet.

In a Montessori classroom where the children are all working at their "maximum plane of development" and therefore doing different things, the "structure" revolves around rules and procedures so that they can all be doing those different things, but still learn.

For example, since most of the work is initially done with manipulatives, a "structure" needs to be in place as to how to share the materials, work with them, and put them away.

There is also a "structure" in place  to make sure all the children are working. In our program each child has a written work plan with a list of jobs that they specifically need to complete. During work time, as the jobs are finished, the children record it on the plan. Written work is placed in a folder for the teacher to correct, while manipulative work is left on mats for the teacher to review.

As the teacher corrects and reviews the work, she marks off which jobs have been done in her grade book. In her observation book she then records information about each child's understanding and progress on the concepts. Simple mistakes are corrected with the child either on the spot, or the next day. While deeper misconceptions that require a review of the concept or a different material, is recorded in the lesson plan book. Additionally, the need for a more advance lesson or new topic is also recorded. New lessons usually presented the next work period.