Revealing mistake: The first scene where they are trying their homemade bobsled, right after coach tells them they need 6 seconds flat, they use the same scene when Junior flips over the bobsled (3 times) but from different angles. Twice when coach is timing them and again right after where they are pushing coach in the VW bug. Junior flips over and lands on Brenner, and Sanka does the same 2 spins and lands on his knees. (00:26:45 - 00:27:20)
Revealing mistake: When Junior inadvertently trips Derice and Yul Brenner in the trial run, it's clear that his legs do not come in contact with either men; the actors just threw themselves to the ground. It's particularly noticeable due to this shot being played in slow motion.
Answer: The events depicted in Cool Runnings of the improbable Jamaican bobsled team were actually quite accurate, according to this page http://www.factmonster.com/spot/02olcrunnings.html.