Spanish has several situations in which it may not be obvious whether a singular or plural verb should be used. These are some of the most common such cases.
Collective nouns - ostensibly singular nouns that refer to a group of individual entities - can be used with either a singular or plural verb for reasons that aren't always clear.
If the collective noun is immediately followed by a verb, a singular verb is used: La muchedumbre piensa que mis discursos no son suficientemente interesantes. (The crowd thinks my speeches aren't sufficiently interesting.)
But when the collective noun is followed by de, it can be used with either a singular or plural verb. Both of these sentences are acceptable, although some language purists may prefer one construction over another: La mitad de habitantes de nuestra ciudad tiene por lo menos un pariente con un problema de beber. La mitad de habitantes de nuestra ciudad tienen por lo menos un pariente con un problema de beber. (Half of residents of our city have at least one relative with a drinking problem.)
By itself, ninguno (none) takes a singular verb: Ninguno funciona bien. (None function well.) Ninguno era fumador, pero cinco fueron hipertensos. (None were smokers, but five were hypertensive.)
When followed by de and a plural noun, ninguno can take either a singular or a plural verb: Ninguno de nosotros son libres si uno de nosotros es encadenado. Ninguno de nosotros es libre si uno de nosotros es encadenado. (None of us are free if one of us is in chains.) Although some grammarians may prefer the singular form or make a distinction in the meanings of the two sentences, in practice there doesn't appear to be any appreciable difference (just as the translation of "none of us is free" in the translation might have been used with little if any difference in meaning).
Nada and Nadie
Nada and nadie, when used as subject pronouns, take singular verbs: Nadie puede alegrarse de la muerte de un ser humano. (Nobody can rejoice in the death of a human being.) Nada es lo que parece. (Nothing is what it seems.)
Ni and Ni
The correlative conjunctions ni… ni (neither… nor) is used with a plural verb even if both of the subjects are singular. This is different from the corresponding English usage. Ni tú ni yo fuimos el primero. (Neither you nor I was the first.) Ni el oso ni ningún otro animal podían dormir. (Neither the bear nor any other animal could sleep.) Ni él ni ella estaban en casa ayer. (Neither he nor she was at home yesterday.)
Singular Nouns Joined by O (Or)
When two singular nouns are joined by O, you usually can use a singular or plural verb. Thus both of these sentences are grammatically acceptable: Si una ciudad tiene un líder, él o ella son conocidos como ejecutivo municipal. Si una cidudad tiene un líder, él o ella es conocido como alcalde. (If a city has a leader, he or she is known as the mayor.) However, the singular verb is required if by "or" you mean only one possibility and not both: Pablo o Miguel será el ganador. (Pablo or Miguel will be the winner.)