[Try_Freedom]

"Weren’t we looking for “would have” or “could have”?"

I beg your pardon? I'm not sure what you're saying.

[Dianna]

I beg your pardon? I'm not sure what you're saying.

Correct: We should have gone to the store yesterday.
Correct: We should've gone to the store yesterday.
Incorrect: We should of gone to the store yesterday.

Because the contraction sounds like "of" when spoken, I think people have forgotten that the contraction stands for "have".