Some of the style guides that I have are categorical in claiming that the plural verb is correct in such constructions as:
One of the things that makes/make him great is he brings it every
night.
Follet in Modern American Usage (p298) states:
These words (one of the [plural noun] who .. ) introduce the most
widespread of all defiances of rudimentary grammar: the coupling of a
plural subject with a singular verb.
Partridge in Usage and Abusage (p214) states:
The rule is that the formula, one of + plural noun, requires the
ensuing verb to be plural.
The Right Word at the Right Time (p405) states:
The construction one of those who or one of the Xs that often presents
the writer or speaker with a problem: does the verb that follows go
into the singular or the plural? ... The answer is the plural: who or
that refers not to one but to those or the Xs. (* See below)
Garner in Modern American Usage (p590) writes:
This construction requires a plural verb in the relative clause, not a
singular one.
Other style guides offer a more nuanced approach. For example, the conclusion after a lengthy discussion of the construction in Merriam Webster's Dictionary of English Usage (p690) is:
So the choice of a singular or plural verb ... is a matter of notional
agreement: is one or those (Xs) to be the master? .... There is
abundant evidence that one has controlled number in modern English
sentences from Shakespeare to James Kilpatrick, and there is likewise
abundant evidence that those has controlled number in other
sentences. Addison was not troubled by using both constructions. You
need not be more diffident than Addison.
Peters in The Cambridge Guide to English Usage (p394) states:
For most writers the choice depends on whether you're thinking of a
single case or a general principle. Usage commentators in the UK and
the US have been inclined to say it should be the plural; and the
Harper-Heritage usage panel voted heavily in its favor (78%). Yet Webster's English Usage (1989) found ample American evidence for the singular construction, and it's just as common as the plural in
British data from the BNC. Writers using the singular take their cue
from one, whereas plural users are responding to those [people] or
the [things].
Finally, Steven Pinker, in his recent The Sense of Style (p250) writes:
For more than a thousand years the siren song of the singular one has
overridden the syntactic demand of the plural those, and writer after
writer has gone with the singular.
...
Usage guides today suggest that either the singular or plural is
acceptable in this construction, depending on whether one or those
looms larger in the writer's mind.
It is interesting that one of the sentences that The Right Word at the Right Time lists as ungrammatical is the following:
If you are one of those listeners who is alternately worried and
puzzled by the state of modern English ... .
This sentence was written by pre-eminent British linguist Professor David Crystal.