I think this error is only difficult for people with certain dialects.
Regardless of where the problem originates (Freud would probably blame our parents), I see this error in lots of people’s written and spoken English.
I’m stretching my brain to think of any instances in which the preposition “of” would follow the verb “should,” and I can’t think of a single instance when that occurs in the English language.
So to make the answer short and sweet, it’s should have.
Pretty much always, I think. (If you can think of a time when “of” would follow “should” in English, feel free to leave a comment explaining your thoughts.)
You should also use have with the following:
- could have
- would have
- might have
- must have
Again, I’m really wracking my brain, but I can’t think of any sentences in which “of” would follow those verbs.
We use of to make connections between things:
- There are three stacks of books.
- There are turquoise blue books at the top of all three stacks.
- Some of the books have hard bindings.
You can find this rule on the Word Choice page in English Emporium, so if you ever forget the rule, come on back!