Jon's "intrinsic field" has been removed due to an accident that sent his atoms flying leaving him with barely enough control over his DNA structure. Over time he was able to reevaluate his physiology and become Doctor Manhattan, a quantum being of nearly unlimited power.
Limited only to his perception of time, Jon can clearly see his future and past from a third person perspective. Likewise, he can grant others with the "atemporal" vision.
A product of his Chronokinesis, Jon can see his own future in a theoretical sense. This power has been blocked by theoretical particles called tachyons.
Able to restructure himself after the removal of his intrinsic field, Jon is not limited to use this reconstruction power only on himself. He's taken apart most inanimate objects and even taken apart human beings as well as reconstructing martian sand into large glass structures.
Jon doesn't need to touch or hold things in order to change their elemental structure, he doesn't even need to be solely conscious of his projections.
Energy Construct Creation
It is unknown whether some of the creations he makes it the manipulation of matter, molecules or entirely creative quantum energy constructs. He's stated he wishes to create his own life after manipulating matter on Mars as a sort of test.
Only seen as levitation, judging by Jon's slow and methodical process it can be termed that he could achieve must faster and dramatic appearances of flight but merely limits himself to hovering.
Never seeming to age, Jon has never appeared any older both physically and mentally after his accident. He's stated that the world grows older around him.
While in microscopic size, superhuman heights or in a seemingly normal form he has displayed great physical strength such as hurling tanks about, lifting planetary structures and heaving delicate technological equipment about.
Telekinetic in his fabrication of lifting objects he focuses on with his mind, Jon is either limited or limits himself to only use his mental abilities to multitask as he takes apart or reassembles objects living and nonliving.
Bullets and blows travel through Jon, as such he can allow all objects to pass through him without so much as a reaction. He can extend this ability to others and other objects.
Able to remove and reassemble the particles and molecules of any object from one location to another with a single thought. Jon has teleported huge and small objects, people and animals alike.
Able to split and replicate his being, this ability has only been shown on himself. He's become many different completely sentient versions of himself that at first seem to be different entities, but are each a divided consciousness of Doctor Manhattan.
Likewise with his Bio-Fission ability, Jon can bring his sentient copies back into his body without any adverse side effects. It is unknown what would happen if someone were actually able to kill one of the clones, but more than likely nothing would happen to the original.
Able to grow or shrink incredibly fast without a seeming limit. He displays great abilities and focus while at these sizes without a loss of control in any fashion.