Here's what happens:
* The Goblet of Fire is supposed to choose the champions for the Triwizard Tournament. It's meant to be a magical artifact that selects individuals based on their merit and readiness.
* Harry Potter's name is put into the Goblet of Fire when he's not old enough to compete. This was likely done by Barty Crouch Jr. (disguised as Mad-Eye Moody) to manipulate the tournament and force Harry into danger.
* The Goblet of Fire is supposed to be infallible. It's said to be ancient and powerful, and its choices are considered undeniable. However, the Goblet selecting Harry, a 14-year-old, demonstrates a flaw in its "infallibility."
The "mistake" isn't about a specific order of the wands, but rather a failure of the Goblet of Fire to correctly choose the champions. This leads to confusion and chaos, as well as highlighting the vulnerability of even powerful magical objects.