As Joe says, there will be consequences for not being right. It is a common expression. It's use always implies something that something bad will happen if you don't do it. 'I had better fix my car or I might have an accident.' 'You had better put that back or mum will be angry.' It always takes the form 'X had better...' so never: I have better, or I will have better. However you can use a past form: 'He had better have...' 'He had better have been to the doctor before going to work. He could infect everyone.'

It means 'I sincerely hope that he's right'. The implication is that he'll be in big trouble if it turns out that he's wrong.

It can means there are consequence to being wrong.