mature birch trees loosing leaves, leaves have dark spots on them
What you are describing is not unusual for a birch tree. They are prone to many different leaf spot diseases. None of them are very serious and treatment is not necessary. Birch trees can drop a large number of leaves and still be okay. We get this question every year at this time. Sometimes they will even drop the leafless branches but again this is common.
Please refer to the following publication on birch trees,
page three talks about diseases.