Can mild hair dryer burn lead to hair loss or other problems?

The burn would have to be quite extensive to cause damage to the hair follicle. If you experience any mild hair fall out it will likely be temporary.. Just be a bit more careful in the next few months and brush / comb hair more gentily as it might be more fragile now.

The burn you are describing sounds like it is too superficial  to lead to any permanent hair loss.  

It would be unusual for a hair drying process to cause permanent hair damage.  The hair is deep in the wscalp (about 6-7 mm) so the burn would have to go down to that depth.