Is 呆 just a casual description or a medically-related thing
呆  mean "dumb" or "stupefied". 

"呆" in "这个孩子有一点儿呆" modifies a noun, therefore, it is an adjective for "dumb" or "silly" 

"this child has a learning difficulty" means  "这个孩子有一点学习障碍" which is a medical term for such condition

Example of 呆 as "dumb": "呆子" (dumb person); "呆頭呆腦" (dumb looking)

Example of 呆 as "stupefied": 呆了一呆 (stupefied for a moment)