My contribution wasn't clear, yes...
Most analysis methods are unable of measuring some of the elements present in the alloy. Dissolving in a acid won't show the nitrogen contents, probably not the phosphorus nor silicon, and so on. Sparks-and-spectrum don't show properly light elements.
Some elements are desired in some steel, even in small amounts, like nitrogen in Duplex 2205 or boron in some turbine refractory steel.
Other elements are very detrimental, hence not intentional, and must be measured. Phosphorus embrittles steel even in small amounts.
Some alloys specify a very low guaranteed maximum of some elements, like 0.02% carbon in many stainless steels.
Well, other alloys are less varied and exotic than steel, which should provide you the most headaches. Don't lose heart!