fault

We can use the word 'fault' to talk about mistakes and responsibility 

You will often hear children saying to their parents that they are not responsible for something happening eg 'It's not my fault. He did it, not me.' 

If they are late for school they might say to their teacher 'It's not my fault I'm late. The bus didn't come.'

More formally, the expression 'be at fault' can be used eg 'I admit that our company was at fault,. We apologise to all our customers who were affected.'

If you have an old car for example, it my have things that do not work properly and you can use 'fault' or 'faulty' (adjective) to describe this
eg
     There's a fault in the air conditioning.
     The air conditioning is faulty.    

     The water pump is faulty and the engine sometimes gets too hot.
     The mechanic says there's a fault in the water pump. I should get it fixed.

You can use the adjective 'faultless' to mean perfect.

For example: 'Your English is faultless. Were you born in Britain?'  

(Of course even people who learn English as their mother tongue make mistakes!)