Big mistake, large error. 'Large' sounds a bit more formal, so is paired with the word 'error' as that does too.

'Big error' and 'large mistake' aren't wrong. They're just rarely paired that way.

EDIT.

They're also far easier to say. It's harder to say 'big error' than it is to say 'big mistake'.

I think big mistake would be most common.

I guess you could say a big error too.