Here is the corrected version. The 10 corrected errors are bolded and marked with asterisks (*). Essay parts are named and transition words underlined. At the end of the essay there is an example of a summary.
(Your summary will be different. That's fine. Just check that you have included the main ideas and kept your summary short.)
[Introduction:] Hitler knew he wanted to “free” Germany from its Jews, including its Jewish scientists. [thesis:] However, he probably never imagined the far-reaching implications of that decision. It led to the United States getting the atomic bomb, and eventually to the nuclear arms race.
One of the first laws Hitler's government passed when it came to power in Germany in 1933 forbade people with any Jewish grandparents from working for the civil service (government), including the universities. His party was proud of German science, and wanted to keep it “pure” from the strange thinking introduced by Einstein and others.
This law led to many brilliant scientists losing their university jobs. Many also realized that as Jews they were unwelcome and possibly at risk in Germany. Some left immediately for university positions in Great Britain or the U.S. *Others followed as they realized their danger,*and as Germany invaded much of Europe.
[support:] Many of them had been working to understand the atom. They realized its terrible power if used for destruction—and knew that German scientists were also working on atomic fission. The thought that the Germans might develop* an atomic bomb moved several of them, including Albert Einstein, to send a letter to the American president. They proposed the U.S. government should start urgent research to make a usable bomb before the Germans could.
After some time, the government agreed. It started a massive secret program they called the Manhattan Project. Thousands of American and British scientists worked on it. They were led by Robert Oppenheimer, an American of Jewish background who had studied physics in Germany in the 1920s. Nearly 30 top Jewish scientists who had fled German-controlled (or Fascist) Europe ended up there too, as well as many *Jewish-American scientists who also hated the ideology Hitler introduced and would do anything they could to *oppose it.
[support:] The bomb they developed was ready for final testing in July 1945. It *was far more destructive than they had even imagined. By this time the Nazis had been defeated, but the war with Japan continued. The American government decided to use their new weapon against Japan.
[support:] Many of the scientists who had worked on the Manhattan Project* had hoped the bomb would never be used. As the Cold War began, they strongly urged an end to atomic weapons.
However, the American government felt they needed the threat of atomic warfare to keep the Soviet Union (US.S.R.) from further aggression. Before long (partly due to secrets a very few of the Manhattan scientists had shared with the U.S.S.R. during the war, when it was still in theory an “ally”), it had developed an atomic bomb of its own.
[support:] This led quickly to a nuclear “arms race.” Within a few years Great Britain, France, China, and several other nations *had also made and tested such bombs. *Once scientists understood the principles,* it proved impossible to keep the technology from spreading.
[conclusion:] No one could have predicted all the consequences that followed from Hitler's hatred of the Jews or from the persecution of Jewish scientists.
Those scientists started out developing the atomic bomb in a race against time, since they knew Hitler’s scientists were working on the same project. They won that race, but ended up using the bomb anyway—and transforming the nature of war and the future of humanity.
(If you had trouble finding all the corrections, there are two in the third paragraph, one in the fourth, two in the fifth, one each in the sixth and seventh, and three in the eighth, just before the conclusion.)
Hitler’s anti-Jewish policies backfired when his government expelled Jewish scientists from German universities. Many of them had been studying the power of the atom along with other German scientists. They feared and hated what Germany was doing, and did everything they could to develop an atomic bomb before their German colleagues could. They succeeded, but the Germans had been defeated before the bomb was ready. It was used anyway, against Japan, and led to an atomic arms race that has changed the world.
(This is a partial list. I've had to remove a couple of links as pages are taken offline and they no longer work.)