IIRC, it also has a balcony off the bedroom. Only explanation for the plants outside the window by the kitchen.
A few times the wall opposite the elevator between the apartments has been show. No doors.
There does not appear to be any windows on the walls on that entire side of the building. Not in the hall or either apartment. Possibly abutting a building next door.
Reinforcing what notfrommensa points out: The entrance to Shamy’s apartment is more or less above the main entrance to the building.
None of the building geometry, nor location, corresponds to the building shown in the zoom out of Howard and Bernadette’s wedding.
Note the standard TV stupidity: The small step leading to the back hall in the other apartment. Such nonsensical raised areas in the back of TV sets are all too common for no real world reason. Some places have a small raised step area and then it leads down some stairs. That’s right, I want to step up in order to go down.
And then Sheldon publishes a paper analyzing the drag coefficient of the tassels on flying carpets. 
It would be great if the Nobel went to the Fermi guys and Amy, due to the three-person rule. Then Sheldon’s apoplectic death ends the series.
I agree that the elevator should suddenly start working on the final show.
They go out with a “Big Bang”, they all die in a freak elevator explosion, the elevator having finally been fixed.
Shamy?
Not if you are a celebrity, they seem to be able to get a publisher for any doggerel they claim is a kids book within days.
Sheldon and Amy. Penny gave them that name.
Actually Howard coined it, though Penny was the first one to use it in front of Amy.
The first episode had the rather boring title “Pilot”. No nerdy terminology. The finale should be titled “Anti-pilot” for symmetry.
or “co-pilot”
Shamy.
That sort of portmanteau naming of a romantic couple was very in back then. Remember “Brangelina” and “Bennifer”?
I am curious if this story line is also meant to be an indictment of Celebrity Scientist and Science Explainer culture. Probably not but you can view it that way I think.
I just got around to watching the episode. Loved it! I would actually love to read “The frightened Little Astronaut” – hilarious!