I'm surprised this hasn't come up for me before, but last night I played a game where one Environment Mythos card was in effect (the one that makes all monsters move as fast monsters) and it was replaced by another Environment Mythos card (one that changes two investigator stats -1/+1 respectively). While resolving the "monsters move" part of the second card, I was suddenly unsure whether all monsters should still be moving two spaces or if the new Environment should already be in effect, restoring the monsters to their normal movements. It made quite a difference; I was playing with the Dunwich board, and Environment #1 would really have those critters racing for the vortices.

I ended up going with the first Environment staying in effect through the second card's gate, monster placement, clue placement, and monster movement steps, only being superseded by the new Environment once these tasks had been resolved. Is this how the rest of you do it?

The Mythos Text is the last part of the Mythos card that you resolve, and that's when a new environment will replace an old one. Thus, during monster movement, you would still apply effects from the environment that's about to be replaced.

Additionally, in case you're not aware: if you draw a Mythos card of a type that can't be in play (Ithaqua: weather), you still do everything on the card as normal . The only difference is instead of

"Weather: apply this effect"

the card's text becomes:

"Now discard this card without further effect."

Thomas, you're right by saying that the rules do not cover this directly, but, as Tibs said, every Mythos Card is resolved according to specific steps. If you look at the rules, pag 12, you'll notice that the "Activate Mythos Ability" is step 4 of the Mythos Card resolution, and only at this point the "type" of card becomes significant: hence, if there's already a rumor in play, you don't resolve the new one; if there's an environment in play, you change the old one with the new one (and check for whether the AO you're facing forces you not to resolve the rest of the card); if you have a Headline, you resolve it. So, in this way, the timing for when to apply the new environment should be rather sound.