Yeah, this show cheats. They used modern mirrors instead of bronze mirrors that Archimedes would have used. And that Cannon bit was ridiculous, besides the improbable flame exploding hit part, the guy used modern metal, water tank, pipes, and valves that Archimedes couldn't have access to also.
Just watched the arms/armor episode, and it used video from the 2009 show about the Chinese weapons developed thousands of years ago during the early dynasties, especially for the 'rapid fire crossbow."
Yes, Mythbusters disproved the Death Ray very thoroughly. As for the cannon they fired the ball into the air. It didn't hit anything. At least not that I saw. I may have dosed off.