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.

They search out iniquities; they accomplish a diligent search - The word חפש chaphash, which is used three times, as a noun and a verb, in this sentence, signifies to strip off the clothes. "They investigate iniquities; they perfectly investigate an investigation." Most energetically translated by the old Psalter: Thai ransaked wickednesses: thai failled ransakand in ransaking. To ransack signifies to search every corner, to examine things part by part, to turn over every leaf, to leave no hole or cranny unexplored. But the word investigate fully expresses the meaning of the term, as it comes either from in, taken privately, and vestire, to clothe, stripping the man bare, that he may be exposed to all shame, and be the more easily wounded; or from the word investigo, which may be derived from in, intensive, and vestigium, the footstep or track of man or beast. A metaphor from hunting the stag; as the slot, or mark of his foot, is diligently sought out, in order to find whither he is gone, and whether he is old or young, for huntsmen can determine the age by the slot. Tuberville, in his Treatise on Hunting, gives rules to form this judgment, To this the next verse seems to refer.

They search out iniquities; they accomplish a diligent search: both the inward [thought] of every one (g) [of them], and the heart, [is] deep.
(g) There is no way so secret and subtle to do hurt, which they did not invent for his destruction.

They search out iniquities,.... The Targum adds,
"to destroy the just.''
Either occasions against them, by charging them with sin and hiring false witnesses against them, as did the enemies both of David and Christ; they sought for proper time and opportunity of committing the iniquities they were bent upon, and even searched for new sins, being inventors of evil things, Romans 1:30;
they accomplish a diligent search; diligently searched out the perfect man, and found him; and also false witnesses against him, and carried their point; which was especially true with respect to Christ;
both the inward thought of everyone of them, and the heart, is deep; being full of cunning, craftiness and wickedness, so as not to be searched out and fully known; see Psalm 5:9.

This is further evinced by their diligent efforts and deeply laid schemes.

Iniquities - They study diligently, to find new ways of doing mischief. Deep - Cunning, both to contrive and conceal, and to execute their plots.