Marache 6 mistakes:
10.Ng5 -1.77 (10.Ba3 -0.73)
15.Ba3 -3.63 (15.Bb4 -2.11)
17.Bf4 -5.85 (17.Qd3 -3.91)
18.Qc2 -7.66 (18.Qe1 -5.90)
19.Qe4 -12.21 (19.Qd3 -7.67)
20.Qxg6 #1 (20.Qxd4 -12.73)

In addition, <nimh/rybka> note that moves 10 and 15 are mistakes. (all later mistakes are insignificant as the game is already lost!). the better alternatives to each are development-related :

7.0-0 dxc3 8.Qb3 Qf6 9.Bg5
10.Ba3 Qf6 11.Bxe7 Qxe7 12.Re1 Be6
15.Bb4 Nh4 16.g3 dxc3 17.Bxc3 Rd8

Also, note that Morphy doesn't choose the strongest move but one that is consistent with his style:

8...Bg4 9.h3 Bh5 10.0-0 cxd6
8...dxc3 9.0-0 cxd6 10.Qb3 Nge7
8...cxd6 9.Nxd4 Qe7+ 10.Be2 Nxd4

are all stronger than
8...Qxd6 9.0-0 Be6 10.Ba3 Qf4

but are inconsistent with his "style" (imho!)

What's instructive about this game is that Morphy shows us how to convert this development advantage into a win (within 4-6 moves!)

< The mastakes come as early as 7. e5?! and move 10.ng5?!. Marache apparently was clueless about the notion of Time in chess. Morphy snatches the innitiative quicker than a robber grabs a purse.>

well, in Marache's defense, this notion was not known then! Morphy was the first to demonstrate this concept and it was not until steinitz & lasker codified it in their publications did it become "common knowledge". (based on my limited understanding of chess history)

there's a reason that botvinnik made his comment about morphy and how he taught the world to play the open game. and this one is a seminal game!

<but when you realize that Morphy had to see that AND the queen trap on the other side of the board to allow the move 14 rook for knight exchange, it's pretty amazing>

but .... from 14 to 18, WHT made 3 significant mistakes. it makes more sense that Morphy's style of development first and attack second, meant that _a_ killer combination was going to be available (soon!). but for Morphy to have calculated a tree of depth 5-7 _and_ with all variations where WHT did NOT make the strongest move is at odds with my limited knowledge of how masters think.

And with your army better developed and further up the board than the opponents', combinations are bound to appear.

The star move for me here is 11...Bf5. This develops his last minor piece, blocks the b1-h7 diagonal and joins up the black rooks. The drawback is that it allows white the exchange winning tactic of 12. Bxf5 Nxf5 13. Bh3 Qg6 14. Bxf8 Qxg5

click for larger view

White has won the exchange, but just look at the development of the pieces! Black has four pieces in play to white's one. And white is going to have to spend another move to get his Bf8 to safety. Surely the exchange is not worth that amount of black development?

Black's next couple of moves increase his advantage. 15. Ba3 dc! I love this move. It opens the d file for the black rook to harass the white queen and it temporarily entombs the white knight and Ra1. The only safe square for the white knight is on a3, but that is already occupied by white's greedy bishop.

By the time the play spools to 18...Ncd4 we have almost total black domination. His pieces dominate almost every useful square and the white queen has nowhere safe to run to. She has to stay near the Bf4 or e2 to stop Ne2+ from forking king and bishop. 19. Qc1? is clearly rubbish. 19. Qd1 allows 19...c2 forking queen and knight. And 19. Qe4 allows Morphy's pretty queen sac/ knight mate.