In a recent exchange with an editor, I had to choose between "What matters is the [singular version of phrase X]" and "What matter are the [plural version of phrase X]." My first reaction to the latter option was, "Huh, sounds strange."
Now sometimes sounding strange is good: For instance, it's often good to use less familiar (but apt) imagery -- imagery which is "strange" in the sense of less familiar -- than familiar and therefore cliche imagery. The fresh imagery is more likely to capture the reader's attention, and to convey the message.
But you don't want to focus the reader's attention on a routine transition like "What matters is"; it's therefore best, I think, to phrase such routine items in routine ways -- to use common versions, not strange ones. (Other writers may legitimately disagree, but that was my judgment for my piece.) Yet was I right that "what matter are" is much less idiomatic than "what matters is"?
Google to the rescue: Google reported for me 400,000 results for "what matters is the," 35,000 for "what matters are the" (which I think is grammatical, but for reasons I don't want to get into here), and fewer than 1000 for "what matter are the." Matter settled.
With about 400,000 results, google gives me plenty of cases where the "is" is used in conjunction with a singular version of the phrase, eg "what matters is the trajectory" and "what matters is the system"; you'd have to weed those out in order to make the comparison. Its unlikely google would return a lot of hits with "what matters are the [singular]".
Still, 400,00 is a lot more than 30,000.
If the only concern is that one should "speak gramatically," then say or write, "What matters is that you speak grammatically." But if success might depend on more than just being able to "speak grammatically," then why not, "What matter are a variety of things, including that you make a good personal appearance, that you speak grammatically, that the audience is favorably disposed to your position, that you are not overshadowed by others on the program, and more."
I don't think the opinions of thousands of people who show up on Google are what matters.
The grammar may be a little obscure, but the idiom "what matters" has hardened in the ear, so to speak. So you can't get to "what matter are" either by ear or by good grammar; you can only get there by mistaking the predicate nominative for the subject of "matters," which takes effort.
I have done similar things. Also, if you want to weed out the hoi polloi like John, you could try the same thing in Google Book Search; presumably the level of exposition is higher in published books.
I think one can't make a proper determination based on the information you two have presented, because the correctness of the constructions depends on the complete thought attempted to be conveyed.
The former is people as the group - one idea, the latter is people acting as individuals encompassed by a "group" noun - so it should be "are" instead of "is."
Each is correct is a specific instance. There is a lot of cattle (up for auction, lot number 15). There are a lot of cattle( in that field over there eating the grass).
What is phrase x?
Googling English grammar sites might be worthwhile for something such as this, unless one wants to collect and classify bad English.
There is many.