Coincidentally, I just finished the third book in the Invisible Library series this morning. I agree that the books were great fun, but the author uses fast-moving action to cover up a variety of plot holes.

Irene does flirt a bit with a female character we meet in book 2. We see the same character in book 3. I should mention, though, that that character qvrf ng gur raq bs gur obbx.