1. It was his mistake that he didn't walk the dog on a lead.

2. It was his fault that he didn't walk the dog on a leash.

3. He made a mistake by not using a dog lead.

4. By mistake, he didn't walk the dog on a lead.

5. He should have walked the dog on a dog leash.

6. He didn't seem to pay attention to the pet dog because of talking with his spouse.
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Would you checkt the sentences and correct any errors?

1-4 are fine.

In 5, I'd remove the second instance of "dog".

In 6, I'd replace "because of" with "while".

1. It was his mistake that he didn't walk the dog on a lead. ✅

2. It was his fault that he didn't walk the dog on a leash. ✅
3. He made a mistake by not using a dog lead. ✅
4. By mistake, he didn't walk the dog on a lead. ✅
5. He should have walked the dog on a leash. ✅
6. He didn't seem to pay attention to the pet dog because of talking with his spouse. ✅

All the sentences are grammatically correct and convey the intended meaning. No errors or corrections are needed.