Name for someone whose interest might be to discredit one's results by trying to find hypothetical mistakes?

naysayer

nay•say•er (ˈneɪˌseɪ ər)

n. a person who habitually expresses negative or pessimistic views.

http://www.thefreedictionary.com/naysayer

Other possibilities

cynic

defeatist

killjoy

wet blanket etc.

Such an individual could be described as a cynic, or a cynical and captious person.

Caveat: when expressing such an evaluation to royalty, care must be taken, as unforeseen and quite gruesome consequences can result. First, locate your points of egress. Second, ensure no sharp or blunt objects are within the royal reach, e.g., daggers, scepters, falchions, maces, guillotines, etc. Third, the evaluation should be accompanied with much bowing and scraping.

e.g., "My Queen, I find your rejection of my suggestions for a wardrobe makeover utterly cynical and captious! Ah, of course I mean that in the nicest, most flattering way, your Majesty."

cynical adjective

1: captious, peevish

2: having or showing the attitude or temper of a cynic

cynic noun

2: a faultfinding captious critic (especially: one who believes that human conduct is motivated wholly by self-interest)

captious adjective

1: marked by an often ill-natured inclination to stress faults and raise objections

2: calculated to confuse, entrap, or entangle in argument

(all linked definitions courtesy of Merriam-Webster online)

"Nit-picking" is defined by Merriam-Webster as "minute and usually unjustified criticism". From this comes "nitpicker", someone who engages in nit-picking.

Perhaps naysayer

one who denies, refuses, opposes, or is skeptical or cynical about something

Merriam-Webster