Flat organizational structures are designed to be organic, flexible and low pressure.
In a flat structure, there are very few layers of management -- the chain of command only goes up through two or three people.
Often, an owner makes major business decisions, and a manager or managers underneath the owner supervise employees, who are all equal to one another. This allows for greater coordination, but does have certain disadvantages.
In a flat organizational structure, the layers of leadership are few but leadership tends to be more organic in nature.
Since managers are on equal footing and involved in the same projects together, they may give employees different tasks in a confusing manner. Unless the process is very clear, an employee may be trying to work for two bosses at the same time, leading to confusing and contradictory instructions.
Flat organizational structures can only last so long. As a business grows and eventually goes public, the flat structure cannot stay. A public business needs a board of directors to evolve into a corporation, and a more complex business structure to expand into multiple branches.
In a flat organizational structure, there is very little room for employees to move up through the business. There are advantages to this -- it lowers the problems caused by unhealthy competition. However, the flat structure also makes it harder for ambitious employees to find satisfaction. Some people enjoy working hard toward a promotion, and there is not much opportunity for this in a flat structure.
Just as manager roles can become confused in a flat structure, so can employee roles.
An employee may go to work for a flat organisation expecting to do one job, but find out that pieces of many other jobs are also required as needed. This makes it difficult for some employees to focus and specialise at their jobs.