While I agree with that completely, the coinciding problem that I've run into time and time again is the temptation to accept statistical significance but ignore the size of the effect.

You might see p=0.00001 but if the size of the effect irrelevant, then the statistical significance of the relationship is still not something I care about. Great, orange juice shrinks tumors by 0.000001%. I'm still going with chemo, thanks.