In his rearview mirror, Edward's eyes were on me. He was unquestionably shaking with laughter, as if he'd heard every word Tyler had said. (4.96)
Bella isn't aware of it yet, but Edward can hear what Tyler is thinking. Edward seems to get a great deal of amusement from getting at Bella's thoughts through the other Forks High students.
[Bella:] "I smelled the blood," I said, wrinkling my nose […].
[Edward:] "People can't smell blood," he contradicted.
[Bella:] "Well, I can – that's what makes me sick. It smells like rust...and salt." (5.205-207)
In a scene of great irony, Bella faints at the smell of blood. She does have a unique skill that most humans apparently do not have: she can smell blood.
[Bella:] "Okay, then." I glared at him, and continue slowly. "Let's say, hypothetically of course, that…someone…could know what people are thinking, read minds, you know – with a few exceptions." [Edward:] "Just one exception," he corrected, "hypothetically." (8.189, 190)
Edward's special skill is that he can read minds – well, everyone's mind but Bella's. Why do you think he can't read Bella's mind? Why would Meyer have made that the case?
[Edward to Bella:] He smiled as he deciphered my expression. "Having the advantages I do," he murmured, touching his forehead discreetly, "I have a better than average grasp of human nature. People are predictable. But you…you never do what I expect. You always take me by surprise." (12.112)
Edward has special skills, but he can't read Bella. Since he's had the advantage of knowing the thoughts of everyone he's encountered before, he can tell for certain that Bella is unique. That she's a bit of a mystery is part of her attraction.
He streaked through the dark, thick underbrush of the forest like a bullet, like a ghost. There was no sound, no evidence that his feet touched the earth. […]
Edward: "Running is second nature to me, it's not something I have to think about." (13.202, 228)
Bella is amazed by Edward's speed. For him, the skill isn't even worthy of thought. Edward's speed also makes him a dangerous predator.
Edward: "Regardless," he finally murmured, "I have better reflexes." (13.373)
Edward is talking about his reflexes as they relate to driving. This is another one of the qualities that all vampires share – it makes them better predators of humans. Is there anything that humans are better at than vampires?
[Edward to Bella:] "That's true. [Alice] knows other things. She sees things – things that might happen, things that are coming. But it's very subjective. The future isn't set in stone. Things change." (14.30)
Alice's special skill is her ability to see the future. The skill has a weakness in that the future can change as people alter their plans.
[Edward to Bella:] "Mind over matter," he repeated, smiling his teeth bright even in the darkness. (14.183)
Edward hopes he has the inner strength to hold back his natural instincts with Bella. Though he is physically very powerful, he does often worry that he's weak on the inside.
It was also unsettling to know [Edward] spoke aloud only for my benefit. (16.17)
When visiting Edward's family, Bella is keenly aware that she doesn't have their ability to communicate with Edward without words. Since Edward can't read Bella's mind, they must speak aloud with one another. Interestingly, this means that Bella can keep secrets from Edward, but his siblings and parents can't.
Carlisle, Emmett, and the others turned in the same direction, hearing sounds of passage much too faint for my ears. (17.344)
The Cullens have very sensitive hearing, like many non-humans in the animal kingdom, including dogs. This is yet another skill vampires have that makes them dangerous predators.
I guessed Jasper was using his peculiar gift to control the situation. (18.15)
Jasper can manipulate emotions. He uses this skill to ease the tension of the situation when the human-eating vampire coven appears.
[Laurent to the Cullens:] "You can't bring him down. I've never seen anything like him in my three hundred years. He's absolutely lethal. That's why I joined his coven." (19.106)
James is incredibly skilled at tracking and killing his prey. Though all vampires are proficient predators, James seems to be a step above everyone else.
My guilt slowly subsided as I looked into [Alice's] dark eyes. But, even as the calm spread over me, I knew I couldn't trust my feelings with Jasper there. (20.53)
Because Jasper has the ability to manipulate emotions, Bella can't trust that her feeling of calm is natural. She seems to prefer to feel her true fear and apprehension. Why is that? Should she resist Jasper's influence in this situation?
[Alice to Bella:] "As predators, we have a glut of weapons in our physical arsenal – much, much more than really necessary. The strength, the speed, the acute senses, not to mention those of us like Edward, Jasper, and I, who have extra senses as well. And then, like a carnivorous flower, we are physically attractive to our prey." (20.80)
Like any great predator, vampires have a wide variety of effective weapons. Their physical attractiveness, however, is a weapon designed to be effective on their primary prey – humans.
[Alice to Bella:] "We have another fairly superfluous weapon. We're also venomous," she said, her teeth glistening. "The venom doesn't kill – it's merely incapacitating. It works slowly, spreading through the bloodstream, so that, once bitten, our prey is in too much physical pain to escape us. Mostly superfluous, as I said. If we're that close, the prey doesn't escape. Of course, there are always exceptions. Carlisle, for example." (20.82)
Alice explains another weapon of vampires. This comment foreshadows that last scene in the ballet studio, during which James bites Bella. After being infected by James's venom, Bella is in too much physical pain to escape or even try to fight off her attacker.
Alice looked meaningfully at Jasper. A deep, heavy fog of lethargy washed over me, and my eyes closed without my permission. My mind struggled against the fog, realizing what was happening. I forced my eyes open and stood up, stepping away from Jasper's hand. (21.21)
Jasper is using his special skill to manipulate Bella. He's attempting to help her relax and sleep.