Labeling can help others know what to do and how to help special needs children. For instance, a child might become known as a trouble maker or be punished for something that they cannot control. A special needs child might act out differently or be unable to complete certain tasks. If the child has been diagnosed and labeled, the teacher (or other authority figures) would know how to manage the child in a more appropriate way. The danger is that the child will not rise to their full potential because some teachers and authority figures are too lax in their expectations. It is unfair to expect a special needs child to perform a task they cannot complete, but it is equally damaging to have no expectations or too low expectations.
I would say that the main advantage is that you can then get the special needs students the kind of help they need. The major disadvantage is that you risk them being perceived negatively. You risk having the other kids look down on them and stigmatize them.
As a special education teacher for 12 years, a label to me is just to identify students that need individual attention. The exact label to me doesn't seem to make a difference. Each child/student is an individual, and once they're identified as need additional attention, each student is treated as an individual. Strategies of helping each student then pursue their goals is the intent and rarely has to do with the label.