While reading BD the first time, I was too wrapped up in the plot to notice any similarities. But, I recently re-read AMSND, and I see huge paralells between it and books 1&2 of BD.
*First of all, the obvious - imprinting. It is just like the love spells of the fairies, which is made especially clear by the fact that it's often referred to as 'magical' by bella and carslile.
*Another point that coincides with AMSND- there are two main groups in both. In Shakespeare, there was the group of humans (I'm including Bottom and company in the same lot as Hermia and Lysander) and the Fairies.
In BD, there were also two main groups - The Vamps (and company - bella, etc) and the Wolves/Quileutes.
*In both tales, the main force that brings the groups to meet is love. In AMSND, the unrequited love triangle/rectangle between Demitrius, Lysander, Hermia, and Helena is what gets the fairies to use the love potion in the first place. In BD, the love between Bell and Ed ( and the subsequent consequences of Bella becoming a vampire) are what bring the Vamps and Wolves to be at odds.
*Then, lo and behold - the love potion (and imprinting) get thrown into the mix, and craziness ensues. People who once loathed eachother now find themselves passionately drawn to one another, and in that love both stories find resolution - the human couples in AMSND get their happily ever after, and Jake's imprinting in BD provide a way for both mythical groups to be at peace.
I'll probably come back and edit a little bit later on, just to make sure my post makes sense. Maybe I'm reading into it too much, but these points really stuck out to me!