Faulty pronoun reference means the antecedent of your pronoun is not totally and immediately clear. There is no single rule for making pronoun reference clear in all cases. Most often a reader will try to connect the pronoun with the subject of a previous clause or sentence:
When Andre cut his finger, he screamed out in pain.
But not always, sometimes the reader will connect it with the closest noun:
When Andre cut his finger, it started to bleed.
In both cases the meaning is clear, and so there is no problem. Problems occur, though, when two words compete as antecedents and the meaning blurs:
Finally, he wrapped his finger in a bandage, and it stopped bleeding.
Or when the antecedent is not named explicitly:
The danger of creosote build-up has not been properly publicized by the makers of wood burning stoves. This should be looked into thoroughly.
Or when a pronoun seems to refer back to a single word but is intended to refer to a whole clause:
My brother caught my cold which made me feel bad.
Because "which" seems to refer to both "cold" and the entire base clause, the meaning is slightly out of focus. Careful writers keep the meaning focused by making pronoun/antecedent relationships totally and immediately clear. It isn't enough to say readers who want to understand your meaning will if they work hard enough. Your reader should connect your pronoun with its antecedent at once.
To make the reference clear you could change the wording slightly:
The danger of creosote build-up has not been properly publicized by the makers of wood burning stoves. This lack of publicity should be looked into thoroughly.
You may want to re-word the entire sentence and eliminate the pronoun:
I felt bad that my brother caught my cold.
First, notice the problem, and having seen it, eliminate any ambiguity.