Mixed constructions often happen when you start a sentence with one grammatical structure and then switch to another.
INCORRECT: For most people who have pets live longer, happier lives.
This sentence seems to be going in one grammatical direction, but suddenly switches to another without warning. It can be revised a few different ways:
CORRECT: For most people who have pets, life is longer and happier.
CORRECT: Most people who have pets live longer, happier lives.
Another instance of mixed construction is when the subject and the predicate7 of the sentence don't make logical sense together.
INCORRECT: The court decided that the woman's welfare was not safe with her abusive partner.
The woman is who should be safe, not the welfare. Revise:
CORRECT: The court decided that the woman was not safe with her abusive partner.
A much more specific mixed construction happens when an appositive8 and its noun do not agree.
INCORRECT: Doctors, an honorable profession, requires a great attention to detail and a lot of memorization.
Doctors are not a profession, medicine is. Revise:
CORRECT: Medicine, an honorable profession, requires a great attention to detail and a lot of memorization.
7Predicate is "the grammatical term given to the verb plus its objects, complements, and adverbial modifiers" (Hacker 484).
8 Appositives are words or word groups that rename nouns.