What are symptoms of a breastfed baby having an intolerance to moms dairy intake?

Milk intolerance. While this can happen it is hard to prove. The usually reported symptoms are fussiness after breast feeding, perhaps somewhat like colic, diarrhea, possibly vomiting (unusual). The test you can do is to eliminate cow's milk for a week and see if it makes a difference (but you will need to supplement the calories, vitamins, fats and proteins with something else).