In my experience, there are roughly two kinds of open theists: Some have a more exegetical center of gravity (e.g. Boyd, Sanders) while others have a more philosophical center of gravity (e.g. Rhoda, Hasker, van Inwagen). My email is most directly applicable to the first group.
From my reading (and I haven't kept up with all the current open theist literature), the open theist definition of omniscience parallels the standard definition of omnipotence. Just as the definition of omnipotence is consistent with God's inability to do what's logical impossible, the definition of omniscience is consistent with God's inability to know what's logically impossible.
From my reading, open theists claim God knows all about the past, as well as knowing all possibilities or counterfactuals.
Having set the stage, Jer 32:35 is a popular prooftext for open theism:
They built the high places of Baal in the Valley of the Son of Hinnom, to offer up their sons and daughters to Molech, though I did not command them, nor did it enter into my mind, that they should do this abomination, to cause Judah to sin.
But on the face of it, the wording suggests that this possibility didn't occur to God.
Perhaps an open theist could try to gloss that by saying it just means God didn't expect it.
But that's not quite what the passage actually says, and given that open theists accuse classical/Reformed theists of failing to take Scripture at face value, I'm not sure open theists can make that hermeneutical move in good faith.
But here's a more interesting case:
God forgets His people’s sin for God’s own sake (Isaiah 43:25).