Every piece can be gotten as soon as you get to the room where it is. You don't ever get new abilities later that you can take back with you to earlier levels. That said, don't get hung up in one place forever. They made it easy to open all the levels for a reason. They didn't want people getting frustrated and giving up.
not entirely true. every piece except two can be gotten immediately, the two before the first "hunt" are obtainable only after you get the "hunt" piece, so you have to backtrack a room
the only qualm i had with the game is that i haven't the foggiest idea
what the story meant
yahtzee's thing about the key breaking actually makes sense. in an area where going right makes time go forwards, and left makes time go backwards, you can't unlock a door from the right hand side because as you unlock it you're moving left and time goes backwards, meaning it relocks as it unlocks and your key is wasted
Gaming World Forums
Braid on XBLA