What is interesting about the interior spaces of Gatsby's house? How does Fitzgerald use interior space to help us further understand Gatsby's character?

Gatsby's house characterizes him in several ways. Most obviously, it is his chief vehicle for displaying his opulent wealth. However, the interior also shows how Gatsby fails to get his disguise as a gentleman completely in place.
The first time Nick attends one of Gatsby's lavish parties, he and Jordan stumble on Gatsby's library. Nick describes it as a Gothic-style room paneled in English oak. Nick speculates that Gatsby bought it from a "ruin" in Europe and had it shipped over.
In the library, Nick and Jordan meet the owl-eyed man, who informs them that, to his surprise, all the books in the library are real, not made of cardboard. This causes the owl-eyed man to say:

It’s a triumph. What thoroughness! What realism!

However, he also notes that the pages of the books are uncut, meaning Gatsby has never read them. In this way, Gatsby's disguise as a well-educated gentleman is shown to be a fraud. This characterizes Gatsby as a man who can strike a pose, but not quite pull it off, because he can't get the details exactly straight. The library is similar to Gatsby's pink suits: not quite right. Therefore, people like Tom Buchanan can see through him and treat him with contempt.