Since it is impossible for me to circle and make arrows here, I will answer by stating what is what.
Answer:
1. subject: Sara and Desmond; 
verb: is organizing; 
error: is --> are
2. subject: many of my classmates; 
verb: are arriving
3. subject: the party;
 verb: start; 
error: start --> starts
4. subject: each of us; 
verb: are bringing; 
error: are --> is
5. subject: mike; 
verb: have been trying; 
error: have --> has
6. subject: Mike; 
verb: does . . . get; 
subject: he; 
verb: like; 
error: like --> likes
7. subject: all the funny things; 
verb: is; 
error: is --> are
8. subject: Soo Min; 
verb: is making; 
subject: Maria; 
verb: is buying
Explanation:
The subject is the topic of a sentence, that is, what the sentence is about. The verb refers to the subject, expressing an action or a state/condition of that subject. For that reason, the verb and the subject must agree, that is, if the subject is singular, the verb should also be singular; if it is plural, the verb should also be plural.
Let's take sentence 5 as an example:
5. Mike, like many other students, have been trying to decide on the best gift to buy.
The phrase "like many other students" is what makes the sentence confusing. "Students" is a plural word and, because it is closer to the verb, we feel like using a plural verb as well. However, the subject is "Mike", which is a singular proper noun. Therefore, we should use a singular verb to agree with it. The correct sentence is:
- Mike, like many other students, has been trying to decide on the best gift to buy.