Baseball, by the Rules

It's a little blurry, but this shows a ball thrown by catcher Alejandro Kirk, of the Toronto Blue Jays, sailing into the outfield instead of going to the second baseman to cut down a base-stealer. Errors that happen during stolen bases are, somewhat stragnely, something that you can't actually search MLB's Video room for right now.
An Error During a Stolen Base
When a runner breaks on a steal, everything that happens next starts with the catcher, who receives the pitch and has to make a snap decision: are they going to try to throw the runner out, or not? Once they make a throw, the ball is in play, and the possibility for an error emerges. Because of the timing involved, it’s rare for an error to be called on the stolen base attempt itself, no matter what the outcome is, unless the ball beats the runner to the base by several miles, and the fielder who would've made the tag just straight-up drops it1.
Instead, an error will usually only be assessed if the runner gets up and takes additional bases. This usually only happens if the throw from the catcher is so off-line that it either sails into the outfield, or if the throw hits someone/something and caroms out into a defensive dead zone. Still, even if the defense doesn't have full control of the ball, an error won't be assessed until the runner gets back up and tries for another base.
This gets scored as a stolen base, plus an error (potentially a multi-base error depending on where things stand when the dust finally settles). Of course, a runner who keeps going after an error can still be thrown out; in these cases, the end result will be a stolen base, an error, and a defensive play that gets the runner out. This proceeds much like you would see on a play where a runner tries to get an extra base on a base hit.