Julia said:

I concur. If you allow picking up clue tokens, but don't deal with the monsters in the location you're moving to, I'd say you're going against the rules. The rules state that you can only pick up clue tokens where you end your movement, and monsters are also dealt with during the movement phase. So if your interpretation of these specific location encounters is that you get a second, little movement phase during the encounter phase, you would indeed be allowed to pick up the clue tokens, but you would also have to deal with the monsters. Albeit you're, strictly speaking, no longer in the movement phase when you're playing the location cards, the encounters do tell you to move. So this is arguably more a matter of how you interpret the rules and the cards.

Yeah, I like Julia's mini-movement phase idea. I'd further say it's analogous to moving with the deputy's patrol wagon, so you get no movement points to spend and you're not worrying about finding a route to your destination. To really make this consistant with the regular movement rules, are we also saying you can trade with another investigator who's already at your destination? (Sorry, I know this last one opens another can of worms, since there's also disagreement over which phases trading can occur in.) Oh FAQ, where art thou? Maybe we need a stickied thread for unanswered questions like these that will always have to come down to player judgment / house ruling.

I can definitely see a case for if the encounter dumps you somewhere, like the Woods for the rest of the turn.  If there are clues there, they will (most likely) be sitting there during the Mythos Phase before movement.  If the encounter brings you back, it's probably best to leave them there.  My line of thinking, and perhaps this is a compromise between the two lines of thought, is that if you go to another location and come back you don't really have time to search thoroughly for clues.  You are simply going to the Woods (as in the example), having another encounter there and coming back.  If you were to stay in the Woods for the rest of the turn (ending your movement), then during the Mythos Phase you can pick up clues.  If a gate opens on you, the Clues are gone since clue token placement comes after gate openings.

Obviously, a case can be made for either side.  I know I'm going back on what I said in an earlier post but this is closer to how we play the game.

Looks like the just-released FAQ settles this question:

Q: When does an investigator pick up Clue tokens on the
board?
A: Investigators pick up Clue tokens in only two cases:

1. During the Movement Phase, if an investigator
ends his movement in an Arkham location or street area
containing Clue tokens, he picks them up after evading
or combating any monsters in the same location or
area. Investigators cannot pick up Clue tokens from a
location or street area and then continue moving.

2. During the Mythos Phase, when a Clue token is
placed in the same location as one or more investigators,
one of them may immediately pick it up. If they
cannot agree who gets the Clue token, the first player
decides.

Note that investigators do not pick up any Clue tokens
when they are sent to a location with a Clue token during
the Upkeep Phase, the Arkham Encounters Phase, or the
Other World Encounters Phase.

Damn Thomas, you beat me to it ;'D I was going to say, "Go check the FAQ!"

Note that while "sent to other locations" is mentioned, nothing is said about immediately collecting a Hypnos clue.

I guess we can assume "no" then?

Good catch, Tibs…but, I'll still have my Investigator's accept Clue Tokens from the Guardian.