I'm not a grammar nazi, but "should of" is driving me up the wall.

Nice one. Who’d’ve guessed.

Not wanting to be purposefully controversial, but language is a tool for communication and as long as it's understood by the target audience, then I'd say it was used effectively.

The English language doesn't have a governing body (unlike say French and Spanish) and so whatever we agree on is correct usage. "Grammatically incorrect" has long been a dog-whistle signifier for elitism (you don't have the expensive education to know what's correct) and racism (the local dialect that you speak isn't our 'prestige' version, therefore you are inferior) and I don't really like to see it. Even when those aren't your intentions when correcting people, it still rankles with me.

Not that I'd write 'should of' on my CV or anything, but it doesn't offend me any on an internet forum.

I’m certainly no grammar freak and English also isn’t my native language but this deives me insane… Same with your vs you’re… it’s soooo easy…

"Should of" is bone apple tea material.

Typing "should of" is a sign of failing to understand the basics of English grammar.

Even as a non native speaker "should of" feels really weird to me, it just doesn't make sense. Is this a mistake English speakers do as well?

I could care less.

Crazy thing is, it’s getting widespread acceptance, and will probably accepted as grammatically correct in a few years.

language is full of idiosyncrasies like this (my favorite is an ekename -> a nekename -> a nickname. see Wikipedia). it's perfectly conceivable that should have would be fully re-analyzed in speech like that, so the proper form of the verb to have would become of after should

Damn I should of known this

ITT: Awful linguistics takes

Golly, I should of known that

shoulda

I had a professor who would use “should of” in speech, probably because he read it so much and internalized it as being correct.

While it is true that "should of" etc. can easily originate from a confusion between "'ve'" and unstressed "of", which sound identical, the statement

"Should of" is incorrect

itself is at least a bit misleading and prescriptivist in its generality.

Interestingly, there seem to be at least some native English speakers who genuinely do say "should of" (with a stressed "of") sometimes. This paper for example argues that people who say "should of" really do use a grammatical construction of the form modal verb + of + past participle. One argument the author mentions is that this would also explain the words "woulda", "coulda" and "shoulda", since "of"->"a" is quite common in general (e.g. "kind of" -> "kinda"), but "'ve"->"a" basically doesn't occur elsewhere (e.g. no one says "I'a" or "you'a" instead of "I've" or "you've"). Another is that the reverse mistake, i.e. using "'ve'" in place of "of" (e.g. "kind've"), is much rarer, which is a clear difference to e.g. the situation with "they're"/"their"/"there", where people use these words in place of the others in all combinations frequently. I recommend this blog article for a much longer discussion.

Also, whether genuine mistake (which it almost certainly is in many cases, although probably not all) or different grammatical construction, YSK that "should of" etc. didn't just become popular recently, but have been used for centuries. E.g. John Keats wrote in a letter in 1814: "Had I known of your illness I should not of written in such fiery phrase in my first Letter.". Many more examples (some older as well) can be found e.g. here or here.

TL;DR: While in many cases "should of" etc. can well be a mistake, originating from the fact that it sounds identical to "should've" when unstressed, there is some interesting linguistic evidence that at least in some dialects of English native speakers really do say "should of" etc. (i.e. in those cases it is not a mistake, merely non-standard/dialectal).