Poly said:Great points, Nineveh.
Also consider 2 Chronicles 2:9.
"For the eyes of the LORD run to and fro throughout the whole earth to show Himself strong on behalf of those whose heart is loyal to Him."
This suggests that God looks for hearts that are loyal to Him.
This is knowable knowledge. Our view of omniscience and omnipresence means that God does continually search hearts and is continually, perfectly aware of all present and past objects of knowledge. We see that the future is not knowable since it is not here yet. I think we are getting on shaky ground to say He does not know some present knowledge exhaustively (could be a valid point of attack by our critics). I do not think He could not know someone's heart or chose to not know this. This is inherent in being an omniscient God. If it was theoretically possible, then some evil could slip under God's radar. He could theoretically miss someone repenting before they got killed, etc.
JWs seem to think that God is confined to a location and sends out angels and his impersonal radar, the holy spirit, to gather info. I think we want to avoid anything that might smells like this.