Factual error: After JD steals Louise's money, Thelma decides to rectify the fact that they're broke by robbing a convenience store in Oklahoma. She holds the clerk at gunpoint, asks for all the cash, and then requests he hand over a bottle of booze. The problem is, due to the liquor laws in Oklahoma, one can only buy 3.2 beer and wine coolers at grocery stores and convenience stores, not "hard" alcohol.
Factual error: As the Highway Patrol officer approaches T&L we see that there is a carrier for 12 rounds of ammo (obviously for a revolver most likely a .38 Spl or .357 magnum) on his gun belt. When he surrenders his weapon we find it is a semi-automatic pistol. The cartridges on his belt would not be compatible with a semi-automatic pistol which he was carrying.
Continuity mistake: When Thelma and Louise lock up the policeman in the trunk they shoot two air holes in the lid. Later the policeman sticks his finger through a hole to point out to the bicyclist where Louise had thrown the keys (surprisingly he could tell from the rather feeble sound what that sound was and where the keys had landed), and the rim of the hole shows that the bullet was shot from inside.