He seems to me, reading this review: Rovelli: Physics and Philosophy to be referring to three effects:
Blurring due to the delay in the light from an object necessarily taking time to travel to our eyes, so there is "blurring" of particular point in spacetime for all observers. So the notion of an exact "now" is gone.
The collapse of the notion of “the present” Rovelli considers to be “the most astounding conclusion arrived at in the whole of contemporary physics”.
Blurring due to GR related time delays near massive objects.
Indeed, Rovelli points out that our entire conception of reality is blurred, necessarily – we can only discern the big events, not the infinitesimally small – and that this blurring effect offers a kind of mediation between the counter-intuitive quantum world and the Newtonian world in which we live.
The book, which I have started to read, is a translation, (so I would allow for that) and Rovelli is definitely, (imo), writing for a wider audience, and in a more literary style than you will normally find in popular science books.
With regard to entropy, I can only offer my own guess: he is trying to include the disorder inherent in thermodynamic processes to all aspects of the reality we experience.
Yuk, that's a bit flowery, sorry, but I think that's what he's getting at.
Read the review linked above, see what you think.