There were grammarians in antiquity, and they analyzed Latin. Several grammarians have studied various aspects of Latin grammar in the modern era as well. I find it hard to believe that modern scholars would be in perfect agreement with the ancient ones. Is there something about Latin grammar that we confidently think we understand now but one or more Roman grammarians misunderstood? If there were several such misunderstandings or discrepancies, what were the biggest or most important ones? The Romans did not have the theoretical framework we have today and were bound to misunderstand something; it is unlikely in any field that modern theorists agree perfectly with ancient ones. Let me exclude etymology from this question and restrict it to other aspects of the language.
These are some areas where Roman grammarians' views of Latin differed from ours (it doesn't necessarily mean that they were wrong and we're right).
Under my first heading, I describe an area of eventual agreement. Under subsequent headings, I describe the disagreements (as well as alluding to some of the areas of agreement).
Declensions and Conjugations
The 1st c. BC grammarian Varro introduced the notion of declensions. By the second half of the fourth century the current list of five declensions (with two subtypes of the third) was already standard. Sacerdos in the 3rd c. AD divided the previously recognised three conjugations into the modern standard of four conjugations, by splitting the third one into two. So by the late Roman period, Roman grammarians had established the systematisation that we continue to use today.
Verbs had five voices
Eleanor Dickey writes of the 4th c. AD grammarian Flavius Sosipater Charisius:
Although Charisius' analysis of Latin is mostly similar to ours, differences include the existence of five voices: active, passive, neuter (i.e. intransitive), common (i.e. passive in form but both active and passive in meaning), and deponent (i.e. passive in form but only active in meaning).
So the notions of transitivity and voice were lumped together in a way that is largely alien to us today. I'm not certain whether all Roman grammarians followed Charisius on this, although the OED shows that this confusion continued through the 15th, 16th, 17th centuries and possibly beyond. (The term "neuter" to mean "intransitive" was still found in the 19th century, but that doesn't necessarily mean it was still being contrasted with "active" and "passive".)
Parts of Speech - Participles, but no separate category for adjectives
Aelius Donatus (4th c. AD) and many other Roman grammarians specified the parts of speech as noun, pronoun, verb, adverb, participle, conjunction, preposition, interjection. (Greek grammarians had a slightly longer list: they included articles and also proper nouns, which they considered a separate part of speech from common nouns.)
Vivien Law writes:
Only when grammarians began to study languages like English, French and German did they find morphological justification for giving [adjectives] independent status [from nouns] ... As for the participle, which modern analysis subsumes under the verb because it is derived from a verbal stem, ancient grammarians argued that since it is a hybrid, derived from a verb but inflecting like a noun, it deserves to be considered an independent part of speech.
Gender - four or more
In the 4th c., Aelius Donatus wrote in the Ars Minor that there were four genders: masculine, feminine, neuter, and common. An example of a common-gender noun was "sacerdos", which can be either masculine or feminine depending on referent. Donatus noted two other special categories: (a) "nouns of three genders", such as "felix", which can mean "happy man", "happy woman", or "happy thing", and (b) epicene nouns, which have a fixed grammatical gender but which refer to living things that can have either natural gender, e.g. "passer" (sparrow), masculine. From Law, it seems that Roman grammarians generally agreed that there were four or more genders in Latin.
Dickey, E. (2016) Learning Latin the Ancient Way. Cambridge University Press.
Law, V. (2003) The History of Linguistics in Europe. Cambridge University Press.