I saw an interesting exchange today between GM Nigel Short and Kasparov associate Mig Greengard on the topic of simuls and the strength of the field. One of the points raised during the discussion is that some players (eg Kasparov) still focus on the overall result, even if it means playing safe and solid chess. Greengard gave Alekhine as an example of an other approach, in that he treated simuls as an opportunity to produce brilliancies. I would agree with this observation, especially as Alekhine could do it in a an almost 'risk free' environment, as the requirement to win games as a means to winning a tournament was removed.
While the following game probably doesn't qualify as a brilliancy, it is still meritorious, as Alekhine played it blindfold.
Alekhine,A - Schroeder,M [B01]
New York New York, 1924
1.e4 d5 2.exd5 Qxd5 3.Nc3 Qa5 4.d4 Nf6 5.Nf3 Bg4 6.h3 Bh5 7.g4 Bg6 8.Ne5 Nbd7 9.Nc4 Qa6 10.Bd3 Qe6+ 11.Ne3 0-0-0 12.d5 Qb6 13.Nc4 Qb4 14.a3 Qc5 15.Be3 1-0