“Hashem is the True Judge, the only One who is really qualified to evaluate our behavior”
actually there are quite a few areas in Halachah that require us to judge our fellow Yid
in determining whether or not to believe Lashon HaRA, in what manner to believe it, whether you may or even be required to repeat it, etc. you need to decide whether the person is a Rasha, whether he does certain avairos, how he does them, does he do tshuva.
in the laws of tochachah, the persons level of observance has to be evaluated, is the aveira meforish in the Torah (eating pork on purpose), does the aveirah involve an open publicized rebellion from the psakim of the Gdolim (ie wearing certain colors, women wearing mens garments as defined by current Poskim).
the Gemorah as you must well know is packed all over with judgements that a common Yid must pass on his fellow and act on it