Being stuck at the doctor's or the dentist office with your children can often be boring for them. While you wait for the appointment to come by, they are flustered by all the waiting and want to do something productive, or more productive than waiting around like this. So, if you take your children along with you, make sure they have an activity to do.
One thing that you can have with yourself on the go is a box of crayon. This box of crayon can be with you throughout your excursions and you can take it out whenever your kid wants to do something productive and has nothing else to do. This would make sure that he keeps busy and you don't have to worry about them roaming around aimlessly, while you wait somewhere.