Is There a Doctor in the House? - S1-E13
Plot hole: Lots of factors here: The doctors end up with the opposite kids that they were supposed to have... Why didn't they simply switch in the first place rather than go through all the drama? Also, the male doctor admits Alice let him in and most likely Alice would have told him first door on the right (like she's given directions in other episodes) to locate Peter. And the biggest question of all is, what doctor would make a house call and not look for their patient rather than just ending up with someone else they were not called to see (remember, each parent called their own doctor to see their biological kid).
Suggested correction: The lady doctor goes to see Peter as Mrs. Brady directs her to Peter's room first. Alice likely knows Peter already has a doctor looking after him, as it can be assumed Carol told her, so she sends the male doctor to Jan's room likely explaining to him that Mike's new daughter is also sick and needs to be checked. As to why they didn't solve this doctor problem to begin with; simply they are still a new family and didn't yet think about this as this is the first time the kids are sick.