Using Pronouns

Tips from Proofreading: Plain & Simple by Debra Hart May, with my own commentary:

• "Noun-pronoun agreement. For the substitution of [a] pronoun for [a] noun to work, they need to agree in number: a singular noun needs a singular pronoun to replace it; a plural noun, a plural pronoun."
• The big debate with this rule comes with the substitution of "their" and "his or her." For example, take the sentence "Each student has to turn in his or her own work." Replacing the noun (student) with a pronoun comes with complications. The traditional English rules say that the pronoun should be "his or her", as in the example. However, many experts have recently started to turn towards the use of "their" in place of "his or her." In this case, the sentence would read "Each student has to turn in their own work." This usage is still hotly contested though, so stick to the original rule.
• "Problems of pronoun case. A pronoun's case tells its readers whether it is acting as a subject in a sentence or being acted upon, as an object. Objects can be direct objects, indirect objects, or objects of prepositional phrases."
• The problem that most writers run into in this area is the use of "and I" or "and me." When a sentence starts with two subjects, the accepted phrasing is "Tim and I..." This rule has been drilled into our heads so deeply that when the pairing becomes the object of a sentence, it is still tempting to use "...Tim and I." However, this is incorrect. If this phrase is used as the object at the end of a sentence, it should be "Tim and me." The same logic applies to "...Tim and myself." "Me" should be used in place of "myself."
• "Ambiguous pronouns (this, that, these, which, it, they, them). Naturally, for pronouns to work at all, they must refer back to a previously mentioned noun. Pronouns used ambiguously leave room for misinterpretation."
• If your sentence has multiple nouns or subjects, or if another part of the sentence could be confused by using a pronoun, it is best to avoid using the pronoun at all. Even though schools teach that repetition is a bad thing, this is not necessarily true in all situations. It is better to repeat a phrase than to lose the element of clarity in your writing. Watch carefully for this mistake as you edit and proofread any draft, as it is an easy mistake to make.