So I'm supposed to get the airship parts from Oberon's estate,
but I'm having a terrible time finding the entrance, even with
the city map in one hand. I run the mouse over the front door
image, and there's no door icon - it's like there's no door at all.

Do you get in through the sewers or something? Or despite the
map, am I looking at the wrong building?

Thanks,
Rikter

there are 2 sections with this estate on and on one of them there is a door which you can't go into. What you have to do is go north of the area your in and entee it there.

Remember to open and close the door gently.