From my testing, if you don't want diseases and to avoid disease bugged settlers, you need to go straight to Concord after the Codsworth portion of Out of Time and grab the holotape in the window. Then set it up. I've found that by doing all my holotape settings ASAP after leaving the vault that everything works smoother. This includes WSFW settings for shelter and auto-assignment.
When i used my previous character with Chapter 2, it seemed like it was trying to fire off too many things and got wonky quick. Settlers got diseased almost immediately and the game lagged badly. So far I've not had as many issues on a new game.
Just finished Well, Well, Well, and the door was bugged for me too. Just walked back the long way but i'm worried this might be an issue as it sounds like the quest will take me back here in Chapter 2.