I noticed that Perplex lasts "until the end of the turn," but other powers have more specific language. Outwit, for example, lasts "Until the beginning of your next turn," while Mind Control lasts until the single free action is completed.

So does Perplex last until the end of your current turn, or does it last throughout the entire turn (i.e., until the beginning of your next turn)? Can I Perplex an opponent's Attack down by 1 so that they'll have a harder time hitting me on their turn?

Perplex last until the end of your turn.

Perplex lasts until the end of the current turn. Attacking an opponent's attack down will not help you on his/her turn as it will have gone back to its base value.

And to be clear, lasting until the end of your current turn is lasting the entire turn. Powers such as Outwit, which last until the beginning of your next turn, are actually lasting the entire round, where a round consists of 1 turn for each player.

So Perplexing up a friendly's Defense is pointless?

yep.

Most often yes. There is at least one scenario where it is not and that's with Energy Explosion. If a friendly character was adjacent to some opponents who you wanted to target with EE you could perplex up the friendly's defense so the chances of hitting him/her would be reduced.