Edited for clarity.

I could see a really interesting story starting with him waking up and just sort of knowing that he had the power to shut down nuclear explosions. No idea where this nuclear explosion was going to be, but knowing if he can find it, he can stop it.

"As most of you know, time travel is one of my favorite motifs. As a result I have dedicated a lot of mental energy to the concept. 

This means I ignore a lot of the physical problems, especially all the different motions that would need to be compensated for. The Earth’s rotation (900 mph), its orbiting the Sun (19 mps), the Sun’s movement (40,000 mph) and, of course, the expansion of the universe."

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This is only an issue with Time Travel that also involves teleporting to another time. In the movies Primer and Tenet, you have examples of Time Travel that do not involve disappearing from one moment and appearing in another. You could have Time Travel where you just basically gain the ability to live life backwards until you get to the time you want to be in. It's much less useful, but it neatly avoids things like having to compensate for all the different motions.