Mistake could be a miscommunication between people an error is a mistake that usually occurs in computers (and that involves numbers) like when you provide a code at the atm machine and it turns out to be wrong it says "error" when a person tells you that they've done something wrong they'll say they've done / there was a mistake when a machine tells you that there's something wrong it'll say error 404 (for example)

A mistake is an unintended or accidental error. Approaching the year 2000, an amazing number of people on the Internet said that the year 2000 was not a leap year, and when I would try to correct them, they would argue about it. That was an error. This year (2016) is a leap year, and I know that. But on February 29th, I completely forgot about it and I wrote "March 1st" on a check. That was a mistake.

There is not a huge difference between them. Normally we use the word mistake if a person doesn't do something correctly. The word error is normally used with technology. So if your computer is acting weird or if you do something wrong on your phone, you might get an error message. You normally would use the word mistake if you are talking about a person. The exception to this rule is we sometimes use the phrase "an error in judgement". This basically means a person made a mistake.

Mistake è più elegante e significa sbaglio, tipo ho fatto uno sbaglio. Mentre error si usa in alcune espressioni più tecniche. Ad esempio in ambito giuridico.