Now firstly I know that 99% of bad player assumptions are down to poor DM planning (maybe not 99% but a portion, to be determined later) but there are times where players see something and latch on to it and go in the wrong direction. An example of this is:
"You enter a Dwarven Stronghold that has been taken over by a Human Archmage a century or so ago. You reach a large door, immediately the whole room glows red and Earth Elementals begin to appear (in rising numbers and in power)"
now you have two options:
1) Fight 10 waves of enemies
OR
2) Use Knowledge (Arcana) to try to unlock the door
and the player's choice
3) Try Knowledge (Dungeoneering) (best I could think of off the top of my head) to try to see how the Dwarves would unlock the door. (and then I roll them a 1 openly or anything secretly)
Now the bad assumption is ASSUMING one way or the other but in this case assuming the trap is a security feature of the Dwarves and not the Archmage.
Now this is only an example but do I tell the players "No it's not a dwarven security system" flatly and without the usual DM's "you don't really know" edge OR do I just let them die in Earth Elementals? (or if there is a Player's Method (you know how they ALWAYS pick option 3) then I would still like to know what you would do to deal with this)
The players suffered through several pointless fights before expending a lot of resources and losing a party member before killing all the enemies, this meant that the Archmage was too strong for them and killed all but one party member (I fudged the second-to-last guys death because I didn't expect anyone to live and then the last guy rolls a 20

)
First, I'm assuming 10 waves is not a winnable situation for the PC's. My first bias would be to put a time limit on the wave of enemies. The runes begin to glow (Round 1), glow brighter (rounds 2 - 4), mounds of earth rise up (Round 5), gradually forming into vaguely humanoid shapes (Rounds 6 - 8), pull themselves loose from the floor/walls (Round 9) and move to the attack (Round 10). Then the trap shuts off until the next wave is to be released. If the players are hurting, and have no idea how to get past the door, then they should back off. The system shuts down (why waste its resources?), and either the existing elementals chase the PC's, or perhaps they return to the stone (again, to maintain materials). If they show no sign of retreating, there's no harm suggesting to a character that they are reminded of an ol mentor, a History check recollection, or some other suggestion of retreating and regrouping rather than grinding their blood and bones against the rocks.
they are there as a distraction to the players while they make Arcana checks to dispel the magic to open the door.
That's exactly my point is that there are runes that the players don't understand, they roll a Knowledge (Dungeoneering) check to decipher the Dwarven runes (except they aren't Dwarven they are Arcane) and never think to check if the runes are Arcane.but the example may be a bad one, the party make an assumption and try to save themselves but the assumption is wrong and they continue to try ideas that aren't what they need to do to conquer the simple lock, how do you deal with this? (I'm guessing from your answer it hasn't come up)
I agree with those noting knowledge is passive. The runes ARE arcane, and a wizard should not need to carefully consider whether these runes might, or might not, be arcane to get a roll. Anyone who speaks Dwarven should be able to see that these are no Dwarven runes he recognizes. Did you have to stop and carefully consider whether Knowledge: Arcana or Spellcraft would open the door, or did you *know* which was appropriate? The PLAYER should not be demonstrating knowledge that these may be arcane, the PC should be - he gets a Knowledge skill roll.
Finally, let's not forget a Lock can be opened with Open Locks - or, at least, the attempt should stand a chance of revealing this is no ordinary lock. Dispel Magic might shut the mechanism (and/or trap) down long enough for the heroes to get past (but now it's back when they want to leave), and Rogues can disarm magical traps. Spellcraft can ID a spell (like Wizard Lock) that is already in place, or an unusual effect with a very high roll. There's not just "one, true way" to address the challenge.
Try telling the players "You're proceeding under a false assumption. I know it was a few sessions ago, but do you remember that scene where <insert assumption-busting information>..."
If you feel that that's too metagamey, ask them all to make Intelligence checks first, then tell the above to whoever rolled highest.
Doesn't have to be that obvious - it could even be giving that high INT check the nudge "what makes you so sure the Dwarves built this?"
interesting, I read that to mean that Knowledge checks don't mean looking through a book for something, just look and think, but you have to think about it.
I can't imagine that surface thoughts are enough to remember that 3000 year old Dwarven King's grand-nephew's name, you have to think "What did I learn in *here* (for example, "What did the old dwarven caretaker say about the family killed during the Great War" but it isn't something you learned an hour ago, it is for things months or years ago, or else you would have to roll a Knowledge check for "What did the old lady send us down here for?" so it won't be stuff you just know, you have to think about it...actually the more I think about it, it should take time
Like most of the other posters, I disagree. Knowledge is "what you know". There is no ability to "consider again" (like the real life racking of one's brain to recall), and there is similarly no need to focus on it. If I ask you the name of the Queen of England, or the first President of the US (pick based on your nationality), do you stop and carefully consider, or do you know the answer?
I would give a character a re-roll with a bonus if he had the opportunity to consult a generic research source. I'd also consider the possibility that, with this research source, it's a matter of time, as the answer is in there (but "he has to roll to pick up the significance" is a valid approach as well).
Or you can dig in your heels, require the players to demonstrate their in-character knowledge before permitting a roll to use that knowledge (which, IME, will eventually result in every issue being greeted with each player listing each of his skills in turn to see if one of them holds an answer), grind them against the elementals and then wonder why they arent happy with your game.