I ran into the same bug with the Doctor's office. I think what caused it for me were these steps:
1. Made the Dr appointment from the office, she says something like "I can use my lunch break for the appointment."
2. Go to the Dr's. He tells you it'll take a couple days for the blood panel to be done.
3. However lunch is still available after the Dr visit, so I went to lunch.
4. Continued the rest of the day, went home, slept, etc.
5. Next day go to the downtown area, the Dr's office is starred up as if an active quest, can't go into work because she says "I should visit Dr Kelly first." Going into Dr Kelly's office gives you the generic NPC talk when they don't have anything active for you like "Hello, Stacy. How are you feeling?" So you can't progress at this point.
Opening up the save file in RPGMakerSaveEdit shows that the "Doctor's Office" switch is on, and the Doctor variable is at 1. I had to edit the switch to off, then I could progress normally. I was able to continue, then eventually got the call to visit the Dr again for the second visit, after which the doctor variable was set at 3. I'm assuming that on the first Dr visit, the flag didn't get properly switched off after the initial visit, and the doctor variable was added at 1 (the variable wasn't present in previous saves) and that made the condition that stopped progress.