Amarande: <WhiteRook48: ran into trouble quickly>
Not really. The loss occurs fairly late compared to virtually all of Morphy's other odds victories, and was a slow process.
Over the course of moves 21-28 Napoleon proceeds to ruin his game. It's not entirely clear why, as unlike most of Morphy's Rook odds opponents, he made no glaring mistakes or clearly bad policy in the early game (other than the usual 19th century tendency to neglect castling); indeed, even with the Rook on a1, White would have only a slight advantage at move 21.
However, after playing the first twenty moves at such a caliber, Napoleon nonetheless managed to drift into a lost game, even though analysis shows that Black was given many "second chances". It is, in particular, nowhere near as clear-cut as Sergeant's "an error leading to sudden and unexpected collapse" comment on 21 ... Nf8 in <Morphy's Games of Chess>.
True, 21 ... Nf8 is indeed a significantly inferior move (21 ... Rd8 seems to be "technically" best, however, even 21 ... O-O is simple and good, and probably would have left Morphy resigning soon as White seems to have no powder left at that point), but even after 22 dxe5 Black still had better in 22 ... dxe5. White can then force Black's King to move with 23 Nd6+ and subsequently open some lines in the center but this does not appear to be sufficient for victory or even a draw.
After 23 ... dxe5 White begins to show the first significant gains - Morphy could have had a draw here if he wanted, by 24 Nd6+ Ke7 25 f6+ gxf6 26 Nf5+ Ke8 27 Ng7+ etc. but this line gives only a draw, so he mixed things up with 24 f6, and it is probably at this point that Napoleon's nerves began to fray. He could have perhaps retained an advantage by 24 ... Ne6, which ultimately leads into a complicated endgame with White's Queen vs. Black's Rooks, or forced a draw with 24 ... gxf6 (after which White really has nothing better than the perpetual with the Knight previously noted), but instead played the inferior Rook move allowing the fork at g7 after which Black appears to have equality at best.
Black's 25th move appears to be the best possible, and on the 26th move there may be some merit in taking on f8 with the King instead of the Rook, but any winning chances Black had were evaporated by this point.
27 Qe3 is inferior, and gives Black some chances at play again, had he played 27 ... Qe7, but instead Napoleon surrendered two full tempi pointlessly by moving the Rook back and forth. He should have at the least tried 28 ... Rg8, after which it is still not clear if White can force a win.
By move 29, though, it is all over - Qe7 is indeed a blunder that allows Morphy to win in a few moves, but even after a better defense like 29 ... Rd1+ it seems doubtful that Black could have saved the game at that point.
One final point: It is actually a mate in *two* after 34 ... Rd7 - by 35 Qxe5+, and mate by Qxe7 or Qb8. I find it interesting that everyone so far has missed this - even Sergeant in Morphy's Games of Chess states that it is a mate in 3 rather than 2 ...