a. Either the editor or the reporters will correct (his, her, or their?) mistake.
and the correct verb form in
b. Either the Thompsons or their lawyer (is or are?) attending the celebration.
Now, in both types of sentence, there are rules that govern the correct choice. You could take the time to memorize and practice those rules. But, really, why bother? These difficult grammatical situations can be avoided.
In fact, here are some of the words I avoid:
1. Lie, lay, sit, and set. I use sit to describe a person or animal resting fleshy portions of the anatomy on a surface. For the other words and uses, I employ an appropriate synonym such as recline, place, put, and the verb seat.
2. Affect and effect used as verbs. Instead of Factor X affects outcome Y, I use a more precise verb, such as X improves Y or Factor X erodes the quality of Y. Instead of Acme effects changes, I use a more precise expression, such as Acme updates its policy on such and such. Affect as a noun means emotionality. Effect as a noun means result.
3. Comprise and compose. The two words are often used synonymously. That synonymy is criticized by certain experts and defended by others, as you will discover if you look up comprise in a good dictionary. I say, just bypass the problem and use include or make up, or if necessary, consist of. The U.S. is made up of 50 states. Fifty states make up the U.S.
As to the sentence above with doubtful pronouns, grammar gurus say it is correct to write, Either the editor or the reporters will correct their mistake. But it is often acceptable to avoid the pronoun entirely: Either the editor or the reporters will correct the mistake.
As to the sentence with a compound subject and hence a doubtful verb--yes, the grammar books favor Either the Thompsons or their lawyer is attending the celebration. But there are other options: Either the Thompsons are attending the celebration, or their lawyer is. If the celebration is old information, I prefer
The celebration will be attended by either the Thompsons or their lawyer.