Revisited: An array of bronze mirrors can set a wooden ship on fire. (From episode 16)
The large scale array simply took too long to light the ship on fire. On top of that the ship only ignited when it was stationary and positioned at less than half the distance described in the myth. The myth was plausible at a smaller scale, however. Flaming arrows were fired from a ballista at the ship, but to little effect. The most effective (and plausible with Archimedes-era technology) method of lighting the ship ablaze was through the use of molotov cocktails.
Archimedes constructed a death ray by reflecting sunlight onto, and thus igniting, Roman vessels.
In order to have any effect, the mirror would have to be impractically large, and even then, the temperature of wood only raised a few degrees. On the Discovery website, however, a challenge was thrown out to the viewers to come up with an experiment to prove it plausible, and so far, a few of the entries seem to have done so. When all the tests were completed the myth was conclusively busted.