Singular or plural noun in a sentence after using both in a related conjunction?

Question

Occasionally when I am writing a sentence, I end up in a situation where I do not know whether to use the singular or plural form of a noun because I used both just prior to it in a conjunction.

For example:

The worst, and one of the most common, problems is […]

One of the most common, and generally worst, problem is […]

Should problem be singular or plural in those sentences? Is there a rule for situations like this? (It certainly doesn’t help that for one of the most common problems is has is instead of are right next to a plural noun.)

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Update

Here is another example which (along with its non-contraction versions) does not fit the currently accepted answer.

JavaScript / Bookmarklets don’t work […]

Bookmarklets / JavaScript doesn’t work […]

In fact, the sentence before the above example with the parenthesized segment is itself confusing as to whether the next word should be does or do.

Answer 1

There are two related problems here. First, the idiom one of the X always has a plural noun as X, even when there is an intervening phrase or modifier, and even if that modifier seems to want a singular head, as is the case with your One of the most common, and generally worst problem[s]. So the simple answer is that problems is correct in both of the sentences given above.

The related problem that you alluded to is the fact that the singular verb is occurs in close proximity to the plural noun problems. This is misleading: the number of the verb is determined by the number of the verb's subject, and the subject of the verb in your examples is One. The fact that one is modified by a prepositional phrase with a plural object does not change the number of the subject.

(There are some exceptions to the rule given above, but none of those exceptions apply to the phrase one of.)

Answer 2

If you strip out BOTH adjectives, you're left with this:

One of the problems is...

So to make the nouns agree, you use the plural, rendering it thusly:

One of the worst and most common problems is

To fix the first sentence, you'll just have to restructure it because you're trying to marry two separate ideas, that it is THE worst (not merely 'one of the worst') and that it is ONE OF the most common.