In Chapter 3 of The Great Gatsby, what purposes do the two digressions (Owl-Eyes in the library and the car wreck) serve?
Both of these digressions are used in different ways by Fitzgerald to highlight various themes that are foregrounded in this chapter. The man with owl-eyes for example is important because he reveals to Nick that the books Gatsby has in his library are not fake, and that, under the surface, they are genuine:
Absolutely real--have pages and everything. I thought they'd be a nice, durable cardboard.
Of course, the importance of these books is in the symbolic way they relate to Gatsby's character: just like his book collection, Gatsby may appear to be fake or assumed to be fake on the surface, but underneath he is genuine and "real."
In the same way, the car crash at the end of the chapter highlights the kind of people who attended Gatsby's parties and the ridiculous levels of wealth they possessed and decadence that they practised. The drunken man who is incapable of recognising that the steering wheel has come loose from his car but still insists on trying to find a gas station. This of course highlights the conspicuous consumption of wealth and greed but also it identifies how Gatsby is separate from this. Note how Gatsby is described after all the guests have left and the car crash has happened:
A sudden emptiness seemed to flow now from the windows and the great doors, endowing with complete isolation the figure of the host, who stood on the porch, his hand up in a formal gesture of farewell.
The juxtaposition of the hilarious incident of the car crash combined with this picture of the isolated figure of Gatsby cements in the reader's mind the extent to which Gatsby again is not associated with the social network that he has chosen to surround himself with.