They search out iniquities - They search deep; they examine plans; they rack their invention to accomplish it. The original word - חפשׂ châphaś - is a word which is used to denote the act of exploring - as when one searches for treasure, or for anything that is hidden or lost - implying a deep and close attention of the mind to the subject. So here they examined every plan, or every way which was suggested to them, by which they could hope to accomplish their purpose.
They accomplish - This would be better translated by rendering it, “We have perfected it!” That is, We have found it out; it is complete; meaning that they had found a plan to their liking. It is the language of self-congratulatlon.
A diligent search - Or rather, “The search is a deep search.” In other words, “The plan is a consummate plan; it is just to our mind; it is exactly what we have sought to find.” This, too, is language of self-congratulation and satisfaction at the plan which they had thought of, and which was so exactly to their mind.
Both the inward thought - literally, the inside; that is, the hidden design.
And the heart - The plan formed in the heart; the secret purpose.
Is deep - A deep-laid scheme; a plan that indicates profound thought; a purpose that is the result of consummate sagacity. This is the language of the author of the psalm. He admitted that there had been great talent and skill in the formation of the plan. Hence, it was that he cried so earnestly to God.