The correct option is B Scan
'Scan' means 'to look at all parts of something carefully in order to find some feature or fault. When placed here, it refers to scrutinizing "the document". Hence the word is suitable for the given sentence and option A is correct.
'Peer' means 'to look with difficulty', for example, 'She peered through the keyhole.' It is not relevant here, hence option B is incorrect.
'Look up' means 'to find a particular piece of information', to research (to find something that you do not know) whereas the "document" is to be checked or examined (here you are not searching in a quest to gain knowledge, but in a quest to find errors) hence C is incorrect.
'See' means 'to perceive by the eye', it simply means 'to look at the document'; but the look is not enough. The sentence means 'to thoroughly go through the document'. Hence D is incorrect.