Here are the corrections for each identified mistake in the sentences:

**8.**
Original: "Because of a high birthrate and considered immigration, the United States population in the late nineteenth century increased tremendously from 31 million in 1860 to 76 million in 1900."
Correction: Replace "considered" with "considering."

**9.**
Original: "For most of their history, especially since the 1860's, New York City has been undergoing major ethnic population changes."
Correction: Remove the apostrophe from "1860's" to make it "1860s."

**10.**
Original: "Rocks have forming, wearing away and re-forming ever since the Earth took shape."
Correction: Replace "have forming" with "have formed."

So the corrected sentences would read as follows:

8. "Because of a high birthrate and considering immigration, the United States population in the late nineteenth century increased tremendously from 31 million in 1860 to 76 million in 1900."

9. "For most of their history, especially since the 1860s, New York City has been undergoing major ethnic population changes."

10. "Rocks have formed, wearing away and re-forming ever since the Earth took shape."