I see the author's use of allusions throughout the text as a sort of secret code to keep literature alive not only in the fictional society but ours as well. Consider, as the previous post states, the sheer number of literary allusions. Most readers of this book are not going to recognize every single one of the sources nor meanings of these allusions. Those who wish to, are going to do some digging and researching. It is almost as if the author wanted this. Perhaps Bradbury himself was hoping his book would lead readers to discovering many more.
Your question picks up on what is an interesting aspect of this novel - the sheer number of allusions that there are to other texts. Obviously, quotes play a major part of this novel, a world where books are banned and therefore illicit material. What is interesting is who uses these quotes and why. It is important to analyse the characters of Beatty and Faber in particular as they use quotes to try to manipulate/bully Montag but also the quotes reveal their character, which is very interesting in the case of Beatty, as his obsessive quote-using reveals his own deep-seated ambivalence about books and the world he is in.
The first quote we are introduced to comes from Latimer and is said by the first victim of the book burning, who willingly burns herself alive "with contempt to them all":
"We shall this day light such a candle, by God's grace, in England, as I trust shall never be put out."
The quote is used to ironically emphasise the "heresy" that this woman is committing by hoarding books whilst at the same time stating her own protest against this society - the fact that she is willing to die with her books rather than live life without them, pardon the pun, speaks volumes.
"Dover Beach" is used in a fascinating way to expose the emptiness of this dystopian world and also reflect on the changes that have happened in this society:
"....for the world, which seems
To lie before us like a land of dreams,
So various, so beautiful, so new,
Hath really neither joy, nor love, nor light,
Nor certitude, nor peace, nor help for pain..."
It is highly significant that Montag reads this poem to Mildred and her two friends, interrupting their watching of the "family" on the screens. This poem in this context therefore cuts right through the superficial nature of their lives and their dependence on simulated relationships, exposing their inner emptiness, which is why Mrs. Phelps begins to cry immediately after the end of this poem.
Hopefully these examples will help you as you re-read the novel and detect more allusions and consider why the author used them and what he is trying to signify through them.