Here are the corrections for the mistakes identified in the passage:

1. **Incorrect phrase**: "increased the size of the USA to a fifth."
**Correction**: "increased the size of the USA by over a fifth."

2. **Incorrect phrase**: "smallest second population."
**Correction**: "smallest population among the states."

3. **Incorrect phrasing**: "such as polar because, mosse and seals"
**Correction**: "such as polar bears, moose, and seals."

4. **Incorrect phrase**: "trapping and hunting are major businesses."
**Correction**: "trapping and hunting are major activities."

5. **Incorrect phrase**: "The largest group of native people live in Alaska is the Inuit,"
**Correction**: "The largest group of native people in Alaska is the Inuit,"

6. **Incorrect phrase**: "who used to be known Eskimos."
**Correction**: "who were formerly known as Eskimos."

7. **Incorrect phrase**: "the city centre was destroyed in an earthquake but the people soon rebuilt the officers and apartment buildings."
**Correction**: "the city center was destroyed in an earthquake, but the people soon rebuilt the offices and apartment buildings."

8. **Incorrect phrase**: "Despite it is only 571 kilometres south of the Arctic Circle,"
**Correction**: "Despite being only 571 kilometers south of the Arctic Circle,"

9. **Incorrect phrase**: "mild weather."
**Correction**: "mild weather for an area so far north."

10. **Incorrect phrasing**: "a considerate number of them fly Into Anchorage international Airport"
**Correction**: "a considerable number of them fly into Anchorage International Airport."

Here is the corrected passage:

When Alaska became one of the United States in 1959, it increased the size of the USA by over a fifth. Yet this huge state, with the largest mountain in North America, has the smallest population among the states. This means that there are still large numbers of wild animals such as polar bears, moose, and seals, and trapping and hunting are major activities. The largest group of native people in Alaska is the Inuit, who were formerly known as Eskimos. Most of them hunt or fish, but some of those living in cities are involved in government work. Anchorage is the largest city in the state, with a population of around 230,000. In 1964, large areas of the city center were destroyed in an earthquake, but the people soon rebuilt the offices and apartment buildings. Despite being only 571 kilometers south of the Arctic Circle, Anchorage has surprisingly mild weather for an area so far north. Because of its remote location, Anchorage attracts many tourists who want to experience life in the wild; a considerable number of them fly into Anchorage International Airport before renting a pilot and setting off into the remote areas of Alaska.