When picking up destination cards, after the initial deal, does the card(s) which the player chooses to discard, have to be from the three he picked up at that time, or can he discard a card which he picked up from a previous turn?
The cards you discard/return must be from the three you drew this turn.
Here's how the rules phrase it:
The player draws 3 Destination Tickets from the top of the deck. He must keep at least one of them, but he may keep two or all three if he chooses. Any returned cards are placed on the bottom of the deck.
It's not so much that you "discard" destination tickets, but rather that you draw 3 and keep from 1 to 3 new destinations. This means that any destinations you were already holding are totally unaffected - you're stuck with 'em.