Here are the corrections for the sentences provided:

1. **Everest was first climbed in 1953.**
- Correction: "Everest was first climbed in *the* 1953." (Typically doesn't need "the," but is stylistically acceptable.)

2. **Last year I visited Mexico and United States.**
- Correction: "Last year I visited Mexico and *the* United States."

3. **Next year we're going skiing in Swiss Alps.**
- Correction: "Next year we're going skiing in *the* Swiss Alps."

4. **UK consists of Great Britain and Northern Ireland.**
- Correction: "The UK consists of Great Britain and Northern Ireland." (Adding "The" for clarity.)

5. **I don't like films that don't have happy endings.**
- Correction: No correction needed. (This sentence is correct as is.)

6. **Someone gave me a book about a history of modern art.**
- Correction: "Someone gave me a book about *the* history of modern art."

7. **Rob and Louise got married, but a marriage didn’t last very long.**
- Correction: "Rob and Louise got married, but *their* marriage didn’t last very long."

8. **The most people believe that marriage and family life are the basis of society.**
- Correction: "Most people believe that marriage and family life are the basis of society." (Remove "The.")

These corrections improve grammatical accuracy and clarity.