What changes does Eckels notice after returning from the dinosaur era in "A Sound of Thunder"?

Eckels is the main character in Ray Bradbury's "A Sound of Thunder". He has paid a lot of money to a company, Time Safari Inc., to be sent back into the past so that he may hunt a dinosaur. The company has gone to great lengths to ensure that the past is not changed in any way as it is thought that even a minor change in the past could result in changes to the present. Eckels panics when he see the T. Rex and steps off the levitating path that the company has provided. He crushes a butterfly with his shoe. When he returns to the present, at first things appear to be the same, except for a faint, odd smell. He notices that a clerk in the office looks somehow different, but he can't pinpoint the difference. Eckels then sees that the signs in the office contain misspellings--but in this new "present", the signs are spelled the way they should be. The clerk, with whom he had had a discussion about the election scheduled to take place, now has the polar opposite opinion about who should be elected. 

These small differences are noticed only by those who traveled back in time with Eckels as the current world diverged from theirs as soon as Eckels killed the butterfly. This story is the source of the term "butterfly effect" to mean a very small, seemingly insignificant event that has unforeseen results.

What changes in the present when Eckels returns from the dinosaur world in "A Sound of Thunder"?

Before Eckels leaves with his safari guides to shoot a dinosaur from the prehistoric past, he says,

If the election had gone badly yesterday, I might be here now running away from the results. Thank God Keith won.

Eckels is so pleased with the newly-elected president of the United States, as is the man behind the desk. He feels that they're all very lucky, saying,

If Deutscher had gotten in, we'd have the worst kind of dictatorship. There's an anti everything man for you, a militarist, anti-Christ, anti-human, anti-intellectual.

He even says that lots of people have called them, asking if they could go back to 1492 if Deutscher did win. The sign above the desk reads,

TIME SAFARI, INC.
SAFARIS TO ANY YEAR IN THE PAST.
YOU NAME THE ANIMAL.
WE TAKE YOU THERE.
YOU SHOOT IT.

While the men are in the past, Travis realizes that Eckels has left the path, and he panics, shouting, "Who knows what he's done to Time, to History!" When they return, Eckels has a vague sense that the outside world looks and feels incredibly different now, and "the immediate thing" he notices is the sign on the wall, which now reads,

TYME SEFARI INC.
SEFARIS TU ANY YEER EN THE PAST.
YU NAIM THE ANIMALL.
WEE TAEK YU THAIR.
YU SHOOT ITT.

It becomes eerily clear that something has dramatically changed the course of human history, and this is when Eckels notices the butterfly he stepped on in the past. Not only have our language conventions changed, but the man behind the desk is now pleased that it is Deutscher who won the election rather than "that fool weakling Keith. We got an iron man now, a man with guts!"

Thus, even our human values and attitudes have changed completely. A monster was democratically elected by what must have been a majority of the population. It must be a new, hard world outside.

What changes in the present when Eckels returns from the dinosaur world in "A Sound of Thunder"?

In Bradbury's celebrated short story "A Sound of Thunder," Eckels travels sixty million years in the past in order to hunt a Tyrannosaurus rex. Before Eckels embarks on the Time Safari, the beloved President Keith has just won the election. Once they arrive in the past, Travis explains the "chaos theory," also known as the "butterfly effect," to Eckels and warns him not to alter the environment. Unfortunately, Eckels completely loses his composure when he sees the massive dinosaur and sprints back to the Time Machine. Eckels happens to run off the floating path and accidentally steps on a prehistoric butterfly, triggering an extraordinary chain reaction that alters the course of human history.

Once Eckels arrives back in the present, he immediately notices that there is a subtle "chemical taint" in the air, and something feels odd about the environment. Eckels then sees that the Time Safari sign is misspelled in a strange manner and realizes that he stepped on a butterfly. When Eckels asks the man behind the desk who is president, the man responds by saying Deutscher won the election. Under Deutscher's reign, America has transformed into a dystopia, where knowledge is censored, religion is banned, and violence reigns supreme. Overall, America's social and political landscape has dramatically changed for the worse when Eckels travels back to the present.

What changes in the present when Eckels returns from the dinosaur world in "A Sound of Thunder"?

When Eckels panics at the sight of the monstrous Tyrannasaurus Rex, the scouts are forced to shoot it themselves. Angry at Eckels for his endangering the lives of everyone, Travis screams at him, pointing to his feet,

It's his shoes! Look at them! He ran off the Path. That ruins us! We'll forfeit! ...Oh, the fool! I'll have to report to the government. 

They are also extremely worried about what may happen to History. For, if any living thing leaves with them. the entire balance of nature is upset. Eckels argues that he has merely slipped in some mud. However, when Eckels and the guides return to the year 2055, although things appear the same at first, there is something different in the air: a chemical taint that is ever so subtle, the man behind the desk is different, there are different colors--"What sort of world it was now, there was no telling." But, the most telling difference is the sign that is spelled very oddly. Then it is that Eckels turns over his shoe and picks away the mud. As he does so, something falls to the floor,

...an exquisite thing, a small thing that could upset balances and knock down a line of small dominoes and then big dominoes and then gigantic dominoes, all down the years across Time. 

It is a dead butterfly. This is the "butterfly effect": If some living thing is removed, there is a chain of events that change the course of history. This change is evinced with the difference in the air, the appearance of things and people. Eckels has changed the present because he has altered what happened in the past.