In the post-Roman world, early Middle Ages, we have the great Isidore of Seville complaining about the decline of the Latin language in book IX of his Etymologies. This complaint is extremely interesting in and of itself, as it shows that by the early 7th century there was a conscience that the language that was spoken was Latin, though we are talking about a transition stage between the dying breath of Latin and the first breaths of Romance languages. I'll quote Isidore, for his input is interesting:

Some say there are four varieties of Latin, that is, Ancient (Priscus), Latin, Roman, and Mixed. The Ancient is that uncouth language that the oldest people of Italy spoke in the age of Janus and Saturn, and it is preserved in the songs of the Salii. Then Latin, which the Etruscans and others in Latium spoke in the age of Latinus and the kings, and in this variety the Twelve Tables were written. Then Roman, which arose after the kings were driven out by the Roman people. In this variety the poets Naevius, Plautus, and Vergil, and the orators Gracchus and Cato and Cicero, and others produced their work. Then Mixed, which emerged in the Roman state after the wide expansion of the Empire, along with new customs and peoples, corrupted the integrity of speech with solecisms and barbarisms

Those last words are firmly aligned with your question, but Isidore of Seville was not the first to complain about the decline in quality of the Latin language spoken by the people. Quintilian, the great theorist of rhetorics from the 1st century makes some remarks on the importance of speaking correctly in book I of his Institutio Oratoria, and decries solecisms and barbarisms. The whole book I is of immense value and gives an enormous insight of the state of the Latin language in his time. I'll just insert a fragment:

First of all, let the offensiveness of barbarisms and solecisms be put away. But as these faults are sometimes excused, either from custom, or authority, or perhaps from their nearness to beauties (for it is often difficult to distinguish faults from figures of speech), let the grammarian, that so uncertain a subject of observation may deceive no one, give his earnest attention to that nice discrimination of which we shall speak more fully in the part where we shall have to treat of figures of speech. Meanwhile, let an offense committed in regard to a single word be called a barbarism.

But of course Quintilian is not the first to complain about the decline in quality of Latin. Gnaeus Naevius, a Roman poet of the 3rd century BC could not be harsher on how Latin had declined, and having an ego the size of mount Esquiline, his epitaph claims that Latin died alongside him, as the rest of the Roman don't speak properly anymore.

If immortals were allowed to weep for mortals,

the divine Muses would weep for the poet Naevius.

And so after he was delivered to the strongbox of Orc[h]us,

Romans forgot how to speak the Latin language

This is strictly for Latin. Someone else may very well intervene with complaints about the decline of other languages like Greek, Arab, Persian, or any other. I frankly hope to see other users provide more answers on other languages.

I'm going to do one better than Isidore of Seville with the great Greco-Roman satirist Lucian of Samosata, one of whose works is The Trial of Vowels. This satire takes the form of a court speech by Sigma (the Greek letter S) against Tau (the Greek letter for T) for infringing on its property. This is in reference to a linguistic phenomenon in Greek in which intervocalic Sigmas were replaced with Taus--perhaps the classic example of this is how θάλασσα/Talassa/The Sea became θάλαττα/Talatta in Attic (although modern Greek retains θάλασσα). The satire is admittedly somewhat untranslatable, but the gist is that Sigma references other cases of phonemic shifting such as lambda (L) and rho (R), humorously mangles words as an illustration of the chaos that could be unleashed by these trends, and ends it by suggesting that Tau be crucified (a crucifix being a Σταυρός/Stauros).

This is all a bit tongue in cheek but there was a real point to it: the Second Sophistic (the "Greek Renaissance" under the Roman empire, to put it very crudely) was as much a movement of rhetoric as it was literature or philosophy, and in particular many within it revered what they saw as the "Attic style" of rhetoricians like Demosthenes, which was believed to be more "direct" and "pure" than the more grandiloquent and flowery "Asiatic style". This sort of movement of trends between more elegant and more sparse styles of writing is common throughout all of literary history, and in this way the Second Sophistic can be seen as a movement towards the clarity of classical Athenian style and away from the elaboration of Hellenistic (this wasn't hegemonic of course, others used the "Asiatic" mode). So the satire is not just about changing pronunciations, it is also about changing styles and fashions in rhetoric.

This is not necessarily the earliest example of this--Quintillian for example has a warning about avoiding the use of words from regional dialects, although in that case it is less snobbery and more a rather useful call for clarity--however, I do believe Lucian's satire is one of the most amusing, so I thought it deserved mention here.

Your question is actually of primary concern for an entire branch of linguistics: historical linguistics (aka philology). Lyle Campbell, a modern authority on this sub-field, details the importance of written complaints about the usage of various language varieties in the past because they provide evidence of language changes that might otherwise be unrecoverable via the comparative method (the primary tool of analysis in historical linguistics). A famous example of this kind is the Appendix Probi, in which Probus (3rd or 4th century CE) lists all of the ways in which people are butchering spoken Latin, in his view. Some examples:

(1) masculus non masclus(2) vetulus non veclus(3) vernaculus non vernaclus

These examples all provide direct evidence that at the time the Appendix was being composed, spoken Latin had a tendency to apocopate (i.e., 'delete') penultimate vowels. Furthermore, Ex. 2 shows that speakers were also drawing connections between the consonant clusters /tl/ and /kl/, perceiving that /tl/ should be 'corrected' to /kl/.

Thanks to u/Tiako for the examples from Lucian's Trial of Vowels--I was unaware of the source, and it is also a stellar example of the kind of evidence a historical linguist would use to pinpoint what changes were underway in a language in days gone by.

Campbell, Lyle. 2013. Historical Linguistics: An Introduction. 3. ed. Edinburgh: Edinburgh University Press.

In Plato's Phaedrus (370 BC) he bemoans how literacy ruins memory since you can just rely on being able to read it later - and consequently reasoned thought:

And so it is that you by reason of your tender regard for the writing that is your offspring have declared the very opposite of its true effect. If men learn this, it will implant forgetfulness in their souls. They will cease to exercise memory because they rely on that which is written, calling things to remembrance no longer from within themselves, but by means of external marks.

What you have discovered is a recipe not for memory, but for reminder. And it is no true wisdom that you offer your disciples, but only the semblance of wisdom, for by telling them of many things without teaching them you will make them seem to know much while for the most part they know nothing. And as men filled not with wisdom but with the conceit of wisdom they will be a burden to their fellows.