KEG: As keypusher has noted, the 6. Nc3 line played here by Pillsbury is better than its more recent reputation. White can get a small edge with this move, though it allows Black an easy route to eliminating White's light-square Bishop.
In the Pillsbury-Schlechter game here, Schlechter equaliazed easily after Pillsbury's unambitious 8. d3 (instead of 8. a4 or 8. Nd5), 9. h3 (instead of 9. Bd2 or 9. Qe2), 10. Ne2 (instead of 10. Bd2) and 11. c3. But Pillsbury obtained a position in which he was comfortable, so the line worked for him.
Schlechter's play was fine until his tepid 17...Bf8 (17. c4 seems indicated).
18. c4: This seems to be best play. As Rosenthal points out in the Tournament Book, had Pillsbury played 18. f4 he would have been in trouble after 18...g6 19. Nh4 (though the proper follow-up by Schlechter would have been 19...Bb7 and not 19...Bd6 as Rosenthal suggests).
21...c4: This move, which Schlechter might have played to advantage earlier, now becomes the source of much of his later problems. It ultimately costs him a pawn and the game. Schlechter should here have held his ground with 21...Rac8.
31. Nc1: One of only two really poor moves by Pillsbury in this game. The plan of moving his Knight to b3, though ultimately successful because of Schlechter's bad 32nd move, was wrong. Much better was 31. Qd3.
32. Nb3: Continuing with the wrong plan. Pillsbury, as on move 31, should have played Qd3.
32...axb4: After this, the roof caves in for Schlechter. 32...a4 was necessary.
33...Rc4: This makes a bad situation worse. He should just have played 33...RxR.
35. Na5: This wins, but 35. Nc5 seems even stronger.
37...Bb5: 37...Qb4 would have lost immediately to 38. d7 QxQ 39. exQ Bf6 40. Nc6, as Rosenthal points out in the Tournament Book. But the text is also bad. Relatively best was 37...Bc8.
38...Bc6: This should have led to prompt defeat (though Schlechter was already lost). 38...Qe8 was the best move left to him, though it would almost certainly not have saved the day.
39. Nb6: Good enough, but 39. Nxe5 is crushing and a move one would have expected Pillsbury to have found in a heartbeat.
40...Bxe4: This move was tantamount to resignation, and Pillsbury finished off the game quickly after this error. If Schlechter wanted to play on in this lost position, he should have played 40...Bf8.
After 44. Bf8+ (44. Bd2+ was also decisive) resignation was well warranted for the reasons set forth by tamar over 13 years ago (!) on this site.