Do you mean "should've"? That's a common contraction of "should" and "have." In many American accents, the difference between "should've" and "should have" is negligible, and will sound like "should of" even though it isn't.
It also depends on the audience and medium, with "should've" being more appropriate for conversational/informal usage. It would be perfectly normal to say something like "he shouldn't've done that," but if I were writing a message, I'd at least expand the last contraction to "have."
I think there's a general perception that many of the common dialects of American English, especially in the South and West, are associated with being less educated. I am not sure where that comes from.
I'm a native English speaker, and my perception is that when someone speaks in a way where they don't use contractions, it seems verbose and stilted; I associate it with being scolded or disciplined, or when someone is speaking sternly to make a point (or out of anger).
E.g.:
"You don't know where you're going, you should've taken a left" - informative/neutral
"You do not know where you are going, you should have taken a left" - critical/scolding
Omitting contractions can result in speech that sounds strange and unnatural in general:
"Shouldn't we go?" -> "Should not we go?"
"Aren't you coming?" -> "Are not you coming?"
"We didn't, but we should've." -> "We did not, but we should have."