Having frequented quite many of Copenhagens many different libraries, I must say that this is one…read moreof the ok+ ones. The building is airy and usually not too crowded and has some decent spots for studying with interesting views of the library hall and reception. It's also fairly clean.
But it's probably too crowded and noisy if you need to concentrate on something (which is usually why I would visit a library, I guess). The noise might have something to do with the "shared" location with Democratic Coffee Bar (which has awesome coffee btw). Might also have something to do with the fact that Borgerservice is also located here. Apparently, Hovedbiblioteket is the place to be!
These days they seem to be working on the interiors a little, so be prepared for drilling sounds! Nothing decent ear plugs can't take care of for you, though..
A quick look at the literature collection, tells me that almost nothing is in it's right place. Communication books are under religion and so on. But the fiction, music and children's sections seem to be in order. Hovedbiblioteket also seems like a nice spot for taking the toddlers and smaller kids, seeing as a fair part of the third floor seems to be specialized for children.
Oh, and the escalators and toilets are often out of order. The first thing, not so much of a problem. The second thing can be a problem.