In addition to hands-free levitation, the blue man also has the mental capacity to see, not just the future, but ALL of time at once, meaning that he could, indeed, prevent tragedy.
You would not even be wrong to call him Manhattan a god as his omnipotence is no exaggeration.
However, much like his precognitive vision of John F. Kennedy’s assassination, he chooses not to intervene and all for one reason which also happens to be his one true weakness.
While I may have said that Dr. Manhattan is a being of unlimited abilities, technically he only possesses two (molecular combustion and omnikinesis), yet there is no clear end to what those strengths allow him to do.