I see that inside FedExProvider you are using ShowNotifications to output errors/notifications. However you are using Debug.WriteLine which is not always good. I also see that there is a Shipment.ServerErrors inside AbstractShippingProvider class, which is already used to store errors from USPS (there is a method protected void AddError(USPSError error)). So I can suggest to use similar logic for all providers and populate Shipment.ServerErrors.
I see that inside FedExProvider you are using ShowNotifications to output errors/notifications. However you are using Debug.WriteLine which is not always good. I also see that there is a Shipment.ServerErrors inside AbstractShippingProvider class, which is already used to store errors from USPS (there is a method protected void AddError(USPSError error)). So I can suggest to use similar logic for all providers and populate Shipment.ServerErrors.