In the sentence from the title, is it was or were?
To me, was sounds weird because there is a plural form coming right after, but were also sounds weird because it is one problem.
In the sentence from the title, is it was or were?
To me, was sounds weird because there is a plural form coming right after, but were also sounds weird because it is one problem.
One of the main problems was the tourists using the wrong passes
*One of the main problems were the tourists using the wrong passes.(ungrammatical)
The Subject of the first sentence is one of the main problems. This noun phrase is grammatically singular. It is also semantically singular. Although the plural word problems is next to the verb, this does not affect verb agreement here. Proximity agreement, where the noun phrase nearest the verb can determine the agreement of the verb, sometimes applies with co-ordinations and lists. For example:
Here the verb seems to be determined by the noun phrase a double bed (don't let this fool you into thinking that this is part of the Subject. The Subject of this sentence is the word there).
There are also situations where the word one in a noun phrase can override the grammatical and semantic plurality of the noun phrase and cause singular verb agreement:
There are also situations where a noun phrase is grammatically singular but semantically plural. In these situations either singular or plural verb agreement is grammatical:
Here one in ten people is grammatically singular but semantically plural (it doesn't refer to an individual, but the proportion of individuals). The agreement of the verb can be determined either by the grammatical number or the semantic plurality.
However, in the Original Poster's example, the grammatical number of the noun phrase is singular, the noun phrase is also semantically singular. There is no co-ordination or negation to complicate the issue. The plurality of the last noun in the noun phrase cannot override the normal agreement of the verb here.
Incidentally, the example (1) above would sound perfectly natural to nearly all native speakers.
To me, was sounds weird because there is a plural form coming right after, but were also sounds weird because it is one problem.
It could sound weird to you, but that's right.
One is a component of your group (the main problems) and it is the subject of this sentence.
The sentence is referring indeed to a specific component (One) of the plural form, hence the correct form of the verb is the 3rd singular person, that is was.
With of the main problems, you're just adding details about which group the subject is part of.
The correct sentence is 'One of the main problems was people doing X'. Here, the subject is the problem 'people doing X' which is singular and hence singular verb 'was' would be used. It may sound weird because we tend to make verb agree with the immediate subject ('problems' in this case).
The verb should agree with the subject one, so you would say, "One of the main problems was people doing X." The phrase main problems, which is where I think you're getting the false sense that you should use were instead of was, is not actually part of the subject because it is part of a prepositional phrase. In as much as it may seem to change the number in a subject, a prepositional phrase is never part of the subject and so never changes the number of the subject. Therefore, despite the seeming plurality of many problems, the subject of the sentence remains a singular one that agrees with was not were.