What would happen if dolphins were treated as people?

In an exciting turn of events, this post has been inspired by @UberFacts! I couldn't have predicted this happening a couple of hours ago, but here we are. This tweet popped up on my timeline earlier, and I think you'll agree that I couldn't have ignored it if I tried:

Some scientists believe dolphins should be treated as non-human "people" with their rights to life. Unlike many animals, they are self-aware
— UberFacts (@UberFacts) November 8, 2013

Dolphins could become part of our actual society, much like the Elves and Dwarves of Middle-Earth! Imagine a world where we walk/swim hand-in-fin with our streamlined peers, chatting and chirruping away with enormous grins stretched across our faces. We'll have such a jolly time! I am literally so excited by this that I wrote a list of how things would change if dolphins got given non-human rights.*