I was one of the guys that got caught by a level. I didnt think i needed one, but after i got one i began disagreeing with it. I believed my eyes and not the level.
After researching ways to verify the level, plumb a scope etc., and multiple checks. Now i trust my level and assume my eyes are deceiving me.
As a machinist, with a point of reference, i could usually clock or align something within 2-3 degrees like buster stated. Sometimes a little better, sometimes much worse. This is in an environment where many things inside the machine were extremely straight or square.
My machine had a renishaw touch probe that would align my part off features i specified and then display the previous position and the difference. In that scenario, its very easy to quantify your individual ability.