word(s) to describe someone judge others by one tiny detail

Unforgiving means intolerant of any mistakes, regardless of size, reasoning, or infrequency. It is often used in contexts like yours:

http://www.dictionary.com/browse/unforgiving

It was unforgiving of him to judge the employee in such a way.

My choice would be hypercritical. The only disadvantage being that lazy listeners will think you are saying "hypocritical".

These people are often negatively characterized as punctilious. In particular, "punctilious implies minute, even excessive attention to fine points." Punctilious can be used as either a positive or negative word.

I'd suggest, unjust

Something or someone that is unjust is just not fair. An unjust boss might fire you the very first time you're late for work.

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