Factual error: Though he's a bastion of knowledge and a member of the museum board, Bruce Wayne completely mangles Egyptian history - twice. He says that King Tut ruled in the 14th Dynasty, and that the museum's mummy was a 14th Dynasty king who ruled in 1500 BC. Wrong on both counts. Tut reigned from 1336-1349 BC. The 14th Dynasty ran from 1773-1650 BC. Wayne would have known that - and so would his well-educated colleagues, none of whom points out the error.
Factual error: Dick Grayson's mini-camera, which is sitting on the bar, takes several shots of the villains from impossible angles several feet away from its location. And though he conspicuously places the camera in plain view, the crooks never notice it.
Factual error: When Bruce, Dick, and Aunt Harriet are looking at the globe, Bruce corrects Dick's mistake about Lima being the capitol of Ecuador and says "No, as you can see, I was right. It's the capitol of Peru." and points to the globe to show him. Based on the position of Europe facing the camera, he's actually pointing to somewhere in northern Canada.