The Dark One, if fully unleashed, has a great deal of ability to manipulate the pattern, but the idea that he wanted to destroy it was only really embraced by Ishmael and the good characters heard him say stuff about it and assumed that's what the end goal was, when he confronted Rand he showed his idea for a remade world, a world where mankind believed they'd defeated him but where he'd destroyed all empathy and love that people felt for one another.
As for powers the Dark One "touches the pattern" of reality, he was imprisoned in another dimension and when the magic users of the setting bored into his prison just the act of doing so caused mental illness and violent impulses to spike all over the planet, escalating to the point where within a few years rape and torture were becoming underground sports, politics routinely grew violent, and people started turning their previously utopian society's mastery of magic and technology towards making really fucked up weapons.
This wasn't just a passive effect though, the Dark One was touching the minds of the masses but also talking directly to certain people, and cults to him started forming across all levels of society until eventually things got into the open and the War of Power started.
How does this play out in D.C.? Well a lot of the magic users are going to immediately realize something is off, places like Metropolis will start looking like Gotham despite Superman's best efforts, Gotham is going to be barely contained anarchy. Short of some serious divine intervention I don't see anyone in D.C. being able to immediately just go and plug the bore, Wheel of Time is a universe with a pretty high level of magic already and none of them were able to deal with it right away either, it's going to take some serious mojo that will take time to gather and prepare, though I'm confident the D.C. universe can eventually do it.