It certainly is a tragic flaw in science that it can't explain everything. And medicine is useless because it can't cure everything, and police are useless because they can't prevent every crime.
Amazingly enough, science has never proved anything.
It must be useless.
Is that supposed to be an illustration of deductive logic?
Or did you forget the /sarcasm tag?
Science has theories and proofs, and often the "proofs" turn out to be incomplete. Sometimes the Laws need to be adjusted, in the face of new evidence.
That doesn't make them "useless" but it does make them fallible. People mistakenly believe science is infallible.
That is the error.
That is why science will eventually "correct" their errors, far more readily than pseudo-science will correct theirs. Pseudo-science is the New Religion.
I assume that any apparent contradictions are either incomplete analysis or errors, and if we keep looking we may get closer to The Truth, i.e. the Grand Unification Theory
As they say on X Files - "The Truth is out there".