I think they're referring to the philosopher Karl Popper's notion of 'falsifiability', the idea that a claim must be possible to proven false to be admissible in a scientific theory.
Think about falsifiable as "veriviable"/"provable". Falsifibility in Patricks sentence stems from scientific theory. From the POV of critical rationalism a thing is never really provable because there always remains a bit of doubt whether the observed result of an action really is a result of that action and not secretly influenced by some unknown variable. But a proper theory is falsifiable, i.e. it can be proven that action did not lead to a specific result.
So think of Patricks statement as "always give concrete, measurable goals".
auto-antonym[0] is a word that means both one thing, and something else that is the opposite of that. This dictionary[1] (second result on google) has definition one meaning the opposite of definition two, thus the word is an auto-antonym.
[1] http://en.wikipedia.org/wiki/Falsifiability