The vocabulary mistake is using the word greatest instead of biggest or largest. Biggest city and largest city can have the sense of largest population or largest in surface area.

The vocabulary mistake in the context provided is that regarding the superlative form of the word ''great'', which is ''the greatest''. It is preferable to use either the superlative form of ''big'' (the biggest) or that of ''large'' (the largest) since both terms are used with reference to SIZE, VOLUME, AMOUNT, etc. 1) ''Largest'': it is preferred when discussing countable or quantifiable objects such as population, area, fleet, number, market share, etc. Furthermore, this term is more academic/formal phrasing and is usually related to the length of something. E.g.: ''This is the largest area we have known so far.'' E.g.: ''I have heard Python is the largest known reptile in the world.'' 2) ''Biggest'': it is preferred when discussing the dimensions of an object, either literal or figurative, as with person, heart, database, sound system, car, success, etc. Furthermore, this term is more colloquial/everyday phrasing and is usually related to the volume/size of something. E.g.: ''My mom says the wild elephant is the biggest animal in the world.'' E.g.: ''What is the biggest mistake you've ever made?'' *HINTS: >> ''Big'', ''large'', and ''great'' can all be used to describe objects. ''He is hiding behind that big tree,'' ''A great tree had fallen across the river.'' ''He's got a large notebook.'' >> When you are describing amounts, you usually use ''large''. ''She made a very large amount of money.'' >> You usually use ''great'' to describe feelings or reactions. ''He has great hopes for the future.'' ''It was a great relief when we finally got home.'' >> You should use ''big'' or great'' to describe a problem or danger, but not ''large''. ''The biggest problem at the moment is unemployment.'' ''Many species are in great danger.'' >> If you wish to show the importance of something, so ''great'' is a better word to be used. ''He was one of the greatest engineers of this century.'' ''We visited the great cities of Europe.'' Hope that helps!

I think there's no grammatical or vocabulary mistake. We often use the word "greatest" as the meaning of "largest" or "biggest". Of course, people often say "largest" in the case, but that sentence is also okay.

In my opinion, "greatest city in Mexico" means the "best" city - the reasons why it's the greatest may be subjective. By saying that it's the "most populous" it becomes a statement of objective fact - there is no ambiguity.

Should be the biggest, not the greatest city, I think.