In connection with the "American superfluous 'of' ", I always think of another similar mistake, "I should of done it that way". Â In the US we pronounce "have" in that position that way, but of course it must be spelled "have", not "of". Â But people who don't write well spell it the way they hear it (naturally enough), and then come across like pitiable ignorami, more's the pity.
I don't think the two "of"s are related, but I always think of them together.
"Should of" is just a misspelling of "should've" Â Â
There are a lot of cases like this. Â People hear "victual" and write it "vittle", hear "voila"" and write "wahla" or hear "teat" and write it "tit". Â If dictionaries are going to include that definition of "of", then they should define "teh" as a specific article.