Pronoun Ambiguity is a type of grammatical error which occurs when it is not clear what the antecedent of a pronoun in the sentence is.
Jane exercised daily with Rose so that she can stay fit.
In the above example, it is not clear, whom the pronoun she is referring to. Is it referring to Jane or Rose?
John visited the restaurant, had some tea, and then recommended it to others.
James and Charlie were waiting for me at the airport. When I arrived, he got very angry.
When the math teacher asked the student for his homework, he looked embarrassed.
Honey and Rose hugged each other and she thanked her for helping her in a difficult situation.
In the above examples, it is not clear to which of the two nouns, the pronoun refers to. This means that the sentence can be interpreted in more than one way, and some interpretations are funny. To avoid these kinds of situations, always make clear the noun that the pronoun refers to.
Vague Pronouns are pronouns which do not have an antecedent at all. For example:
They know that life will be difficult after this year’s budget is passed. (1)
In the University, they don’t tell you everything in the lectures. (2)
Once he joins college, he will know how to conduct himself. (3)
In the above examples, the pronouns do not have an antecedent noun at all. If these sentences were a part of a larger paragraph, then it might be clear what the pronouns are referring to. But in the above stand-alone sentences, they make no sense whatsoever. We use vague pronouns in everyday life, since often the context is clear and so everybody understands what the pronouns are referring to. For example , they in (1) could refer to the people or even the politicians who pass the budget. And in (2), they refers to either professors or lecturers.
However, in written English, you need to make things very clear by mentioning the nouns.