There were plenty of discussions, and a record of some them has survived.
Pronunciation and orthography
We have really a lot of specimens of this, for example from Cicero, Catullus, Quintilian, Varro. Also consider that emperor Claudius tried to reform the alphabet – this must have definitely spurred many discussions between erudite people and grammarians.
Velius Longus (7.58 s. K.) says that "there's controversy about whether equus must be written with one or two u".
Augustin (Conf. 1.29) was ironic about the fact that at his time it was more important to pronounce homines according to grammar rules [i.e. with h voiced] than to love them according to the law of God.
Catullus (c. 84):
Chommoda dicebat, si quando commoda vellet
dicere, et insidias Arrius hinsidias.
et tum mirifice sperabat se esse locutum,
cum quantum poterat dixerat hinsidias.
At least indirectly, the Appendix Probi mentioned in comments. Also the fragmentary Dubius sermo of Pliny the Elder (which according to naturalis historia 1.228 was badly criticized by grammarians); this was not only about lexicon but also other aspects of language.
Cicero (Fam. 16.17) criticizes a solecism from Tiro (thanks @TheHonRose):
I see what you are about: you want your letters also to be collected into books. But look here! You set up to be a standard of correctness in my writings—how came you to use such an unauthorized expression as "by faithfully devoting myself to my health"? How does fideliter come in there? The proper habitat of that word is in what refers to duty to others—though it often migrates to spheres not belonging to it. For instance: "learning," "house," "art,,' "land," can be called fidelis, granting, as Theophrastus holds, that the metaphor is not pushed too far.
Here too we have plenty; consider that there was even a major split among grammarians between analogists and anomalists. Quintilian (1.5.14) talks about the "pexus pinguisque doctor" (!) who dared refuse the irregular but commonly used adsentior (the "correct" form would be adsentio).
Cicero tells us that analogists wanted to abolish the genitive in -um for all 2nd declension nouns, while he and the other anomalists wished to preserve it in frequently used genitives like nummum, sestertium, triumvirum, deum. Similar positions about "-asse" for "-avisse".
As for the first occurrence, you'll find them as early as the IV century BCE in Greece – for example the controversy between analogists and anomalists began in Greece and was later adapted to the Latin language.