Not exactly military mistake, but more like a major mistake in general.

King Fu-Ch'ai of the state of WU being overrun by the state of Yueh.

Fu-Ch'ai had defeated Yueh and instead of exterminating the leading power in charge, he allowed Kou-Chien of Yueh to live. (Of course, great gifts and bribes were given for the survival). Then Fu-Cha'ai allowed his former enemy to influence his actions. Ultimately he ignored the advice from one of his best advisors/generals yet allowed Kou-Chien's propoganda to enter his mind.

The advice of course was to NOT invade the northern state. To finish taking over Yueh because they will eventually cause the destruction of Wu.

Long story short, Wu ended up invading another great state to their north while the Yueh broke alliance and invaded from the south and taking Wu for themselves just as was predicted.