Or is it the sole responsibility of the PhD candidate?

Also, do you have this constant fear that you may have cited the wrong things? Or paraphrased it wrongly : (
What would happen if we did that?; I mean paraphrased or cited wrongly.

"Cited wrongly" can mean two things:
(1)You put the numbering wrong e.g. instead of [11], you put [1].
(2)Or you've paraphrased it wrongly.

: (

It's ultimately your responsibilty. It's your PhD, and you have more time available to spend on this than a busy supervisor.

Don't stress over small errors though. They can be easily and quickly fixed post-viva. And small errors aren't enough for a fail.

After submission people always spot masses of them and go into a major panic! Needlessly.

I see. So, I don't have to feel bad that my supervisor is not checking my work then.

For the second one, I mean for published work, as in conferences and journals.

As BilboBaggins says, it's ultimately the PhD candidate's responsibility. However, the picture is not as clear as that. Most supervisors will want to look at the thesis to ensure the candidate remains on track especially during write-up. It is not in the supervisor's or the University's best interests to have too many candidates fail or end up with major revisions.

My primary supervisor going through my thesis script four or five times and changing his mind on what he thought I should put in was the main hold up to my submission a few years back.

Ian (Mackem_Beefy)

The quality of any work is not only a reflection of the candidate's ability but also the competence of his supervisor. All are equally responsible for the quality of the work and the publication or proceedings resulting from the same.