As long time fan of the series and a completionist this bug is really irritating. After doing a little research I've found that this bug is on ever version of the game and only has a workaround on the PC through the console command.

The Bug: If you had previously acquire a book that is meant for the Miscellaneous quest Fetch me that Book!, as it is being refereed to, through exploration (Which the quest books can be found in a boss level chest at the end of any dungeon) before you start the quest (given by Urag gro-Shub in College of Winterhold) the quest becomes impossible to complete because Urag gro-Shub will not recognize that you have already found it.

I am an Xbox user and the particular book i found was Chronicles of Nchuleft in Ironbind Barrow while i was making my way towards Winterhold. I tried selling my stuff at the store in Winterhold only to find that Chronicles of Nchuleft was a quest item i then looked in my quest log to see if i said anything about the book but there was no mention. I was worried that i was gonna have this book weighing me down forever and then shortly after i meet Urag gro-Shub when asked for the book needless to say i was happy but that when i noticed that he wasn't recognizing that it was already in my inventory. So I tired following the quest like normal I went back through the dungeon and checked the chest the quest marker pointed at but there was nothing in it and the quest marker just stayed there. I returned to him to try again but he still would not recognize hat I had already had it. that is when i realized the only way to finish this quest was to appeal to the game making gods themselves. So please throw a dog a bone Bethesda and fix the minor bug.

Unfortunately, the quest, for you, is now bugged... so will not be fixed with 1.3... However... new instances of this bug (which can happen with all randomly placed quest items)..should no longer happen.
The quest itself is a very very small sidequest.. which doesn't ad story elements and only results in septims or minor rewards... So the only solution is start a game with a new character (the bug should not happen again, because of a radiant quest fix in 1.3)... or ignore the quest... Yes it will stay in your log and you can't drop the book. The book will not really encumber you though (its weight will not be added to your encumberance)

This occurred on a character made after 1.3

That's weird.. they as much told us the radiant thing assigning roles was fixed.. Well in that case I'm afraid my post was not very useful... and I have to give the more disappointing answer... Guess we'll have to wait until january.

As a general tip:
Do not pick up Uniquely named items from boss chests.. (like I said, the fetch me that book quest is not the only quest which can bug out like this) (so don't pick up X's Shield, sword etc.. or books for that matter. Skill books will hardly ever be found in chests)
Leave them.. as soon as the quest triggers the location.. the dungeon/cave/forts enemies should have respawned and the chest will function like it should.

Well i will keep that in mind as my character is still pretty new and i only cleared maybe 4 dungeons and I'm glad to hear that the next patch will be revisiting quest bugs i just hope that it will not force me to make a new character to fix my current problem or maybe ill just start a new character who knows. I really do love this game i just don't want to spend as much time researching wikis to avoid bugs as i do playing like i had to do for oblivion.

I have also learned that if you suffer from the Book Fetching quest that it will stop all the other books that your supposed to find for him from spawning in the world so that's like 20 or so in game books that the player will never get to read which i would say moves this up from a minor bug to problem bug. However if all those books are unique is unknown to me.

I'm suffering from this same bug on 1.3 with Souls, Black and White, but I heard it can happen with any book. Please fix this for 1.4! Amazingly its the only real bug I've encountered in 150 hours with a level 45 char.

Same here, the first and only bug I've encountered which makes it all the more infuriating plus I now have TWO copies of the book and cannot drop either one!!