In this section, Moldvay says:
"A player should not allow his or her character to act on information that character has no way of knowing (for example, attacking an NPC because that NPC killed a previous character run by the player, even though the NPC and current character have never met). If the players get careless about this the DM should remind them. The DM may, in addition, forbid certain actions to the characters involved. The DM should make it clear to the players before the adventure begins that characters may not act on information they don't have. It will save lots of time later."
This can be a tricky policy to implement, especially in an old-school campaign where you want to emphasize player skill over things like class features or "skill checks".
What Moldvay is referring to is more story-based knowledge, however. This can be interesting to monitor if, for instance, you're running "White Plume Mountain" for the fifth time in twenty years. How many players know right where to go to lay hands on Blackrazor? Or which doors will eat you in the "Tomb of Horrors"?
More interesting still is when this comes into play as a result of inter-party intrigue or struggles. This can be as basic as the party thief filching an extra gem from a chest while no one's looking, to something as complicated as one player's character paying to have an other's assassinated. In all these situations, its a good idea for the DM to take an active role in maintaining the "fog of war" - it keeps the story as compelling as possible and helps maintain immersion.
It's not always possible to completely keep player's from acting on prior knowledge though - players can be crafty, and will often go out of their way to look for way to exploit or otherwise act on their knowledge. Such as a character going into another character's backpack "for a torch" or something, because the player knows that character stole his character's healing potion. It might be a good idea to let players know you're going to be on the lookout for such actions, and impose some sort of penalty for infractions, such as a hit on experience points.
From behind the screen it can be more obvious than a player thinks that he or she is acting on prior knowledge. I had an instance where one of my players owned and had obviously read a module I was running - obvious because he was heading in a beeline towards the biggest treasure in the adventure, which was well out of the way and hard to find and get to. When this became obvious to me I discreetly made a couple of location changes - the player was confounded when he didn't turn up the treasure he was looking for, and kept going back to search again. It was hard to keep a poker face during this!
What are your experiences with players acting on knowledge their character's don't or shouldn't have?