I don't have actual numbers, but the use of "don't" in place of "doesn't" is generally seen as being an uneducated thing to say. It comes up fairly frequently in a few places where it is not viewed as much as an uneducated statement. (All of the following are my personal experience, to be clear.)
The most common place where you see it used without comment is among historically poor, uneducated communities having conversations among themselves, in particular among African Americans and rural people. Both groups tend to switch to more standard language when in a more formal setting (school, for instance) or when speaking to someone who does not belong to their group. This is called "code switching," and it is very common among people who speak multiple languages or dialects in a single day.
When I taught as a chemistry teacher at a predominately African American, inner city school some kids spoke in this way to each other between classes but used standard English in class. Now that I teach at a rural, predominately white school, some kids speak to each other in this way between classes and use standard English in class. Others (usually the better students) used standard English all of the time in both schools. At an urban school with a more affluent, mixed race student population, standard English was used virtually everywhere and someone using "don't" in place of "doesn't" probably would have been teased by the other students.
If my student used "don't" instead of "doesn't" I would have a hard time letting it slide, and I am not overly concerned with my students' grammar.
For adults, using "don't" in place of "doesn't" would be a significant mistake in most business or educational settings. The only place where you might see it is with a person intentionally trying to use it so that they could prove to the world how African American/rural/whatever they really are.
As hunter noted in his answer, there are a few phrases where it is used without comment.