NeverAgain: Howard: hang on there, I'm working on an analysis of the whole game with a recent dev build (061015) of Stockfish 6 and with Komodo 9.2; should be ready in a day or two. A sneak peek for you: yes, 24...d4 was that strong (and 24.a3 correspondingly weak, as you already determined) - on move 23 Black's advantage was roughly worth half a pawn; by move 25 it jumped to a pawn and a half.Meanwhile, here are Botvinnik's annotations, translated from the German text in Megabase 2012 (had to use several online translators as my German is rudimentary, so this may not be 100% accurate).
*** start quote ****
1.c4 e6
Korchnoi probably wanted to dissuade his opponent from the positions characterized by the move d7-d5, but Karpov steers for a solid opening.
3.d4
With a transposition into the Queen's Gambit.
3...Be7
In the game Botvinnik-Petrosian, Moscow 1963 (Botvinnik vs Petrosian, 1963) there followed 4.cd ed 5.Bf4 c6 and subsequently Black successfully solved the problem of development of queen's bishop by means of Bc8-f5.
6...b6
A move introduced into tournament practice by Capablanca and Tartakower. Later this was named "The Bondarevski-Makogonov System".
9. Be2
In Baguio in 1978 Korchnoi played 9.Bd3; he also chose the bishop development
to g2. Following this move Karpov thought for 35 minutes.
12.dxc5
A fatal decision. White cannot exploit the hanging pawns on d5 and c5.
<12.Ne5 Nxe5 13.dxe5 Ne4> and White has achieved nothing.
15.Qb1
15.Bg3 was better. <15.Bg3 d4¹ 16.exd4 Bxf3 17.dxc5!>
17. Bg3
White has to acquiesce to the exchange of his queen's bishop. <17.Rcd2 Ne4! 18.Nxe4 dxe4 19.Bxe7 exf3 20.Bxd8 fxe2 21.Rxe2 Rxd8 22.Red2 Qg4> with a clear advantage to Black².
22.Bd3
It is hard for White to generate activity. Korchnoi seeks to bring the bishop to a2 in order to increase the pressure on the d5 pawn.
24.a3
White does not notice the danger. Now the game is decided already. After 24.Ne2 most of the fight would yet lie ahead.
24...d4!
A decisive blow that would not have been possible if White had kept his center pawn d4 on the 12th move.
25.Ne2
White's weak kingside provides a handy target.
<25.exd4³ Bc6! 26.Qc2 <<26.Qc4 Bxf3 27.gxf3 <<<27.dxc5 Bxd1 28.cxb6 Rxc4 29.Rxd8 Bxd8 30.Nxd1 Rc1>>> 27...cxd4>> 26...Bxf3 27.gxf3 cxd4>
28.Nh4
Indirectly covers the g3 pawn. <28...Qxg3 29.Nhf5+ or Ndf5+>
29...Kg8
One of the white pawns is doomed; the game is hopeless for White.
37...Bc7
Threatening mate in three. <38...Qf2+ 39.Kh1 Qf1+ 40.Ng1 Nf2#>
38...Rxb2
Threatening mate again.
39.Rxd3
The fight continues only because both players were in time trouble.
43.Rb5
White resigns. Following the opening, Korchnoi's play was passive and uncertain; Karpov, however, took advantage of almost every opportunity.
*** end quote ***
¹ a weak move that gives White a 
advantage. As it's not forced, Botvinnik probably gave it merely as an illustration (as in "with the idea").
² here 20.Bb5 keeps the balance: <20.Bb5 Be4 21.Qa1=> [-0.15/38 SF6] with 22.Rxd7 to follow.
³ in case it's not clear from the annotations, 25.exd4 must have been meant as an improvement. SF6 does rate it better as well, but not enough to save the game.
Kibitzing
