An error is a mistake. An error means that you erred (you missed the mark/target), and a mistake is simply something wrong. A mathematical mistake. An error in the logic/thinking. Mistaken identity of the suspect/criminal.
Blunder has the sense of stumbling, blundering. Sports people and gymnasts might make a mistake, a blunder, etc.
A shortcoming means that they 'came up short'; i.e. when the results are in, their results are less that other people (less size, less correct answers, less quality).
And a 'stuff up' is slang for a mess, a bad decision, a bad outcome. I stuffed up the cake recipe. I stuffed up in the exam. I made so many mistakes, it was a big stuff up.
etc.
Metal or other cast material can have flaws. There might be a flaw in the casting of liquid iron, or a building design might have a flaw (they put something in a bad position), or they forgot something important.
Error and mistake are the commonest words, and flaw is used most when something is wrong with workmanship.
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