Pictured as holding aloft a lamp as He walks, God searches through the city—Jerusalem, Zion—shining a light to reveal everyone to His judgment. No one escapes the judgment of God. Who is He looking for in particular? He looks for complacent men, like the Laodicean. Just as Hosea uses wine to illustrate the principle (Hosea 4:6, 11-12), Zephaniah also mentions wine though it is obscured in the translation: the words "settled in complacency" are literally "settled on their lees" like the dregs of wine (cf. the footnote on this verse, NKJV)!
Again, the prophet speaks of a prosperous people who had deluded themselves into believing that their physical wealth meant that they were equally rich spiritually. As the years passed, their relationship with God had diminished into lip service and complacency. When God describes them saying things "in their heart," He means a reasoning process that happens internally. A person could not see it with his eyes, but the attitude cannot be hidden from the Judge walking the city with the lamp of truth.
In today's parlance we call their problem "sins of omission." Like the Laodicean, the religious Jew of that day was not on the streets committing horrible crimes like murder or rape or armed robbery. These verses speak about the thousands and thousands of ordinary people who were stagnant and indifferent toward their relationship with God. Their problem was not what they did, but what they did not do.
Nor does God accuse the Laodicean of the more apparent sins in Revelation 3. He is angry with him because of what he is not doing! He is not a true and faithful witness, and indeed cannot be, because of his poor judgment in prioritizing his life. In focusing on his selfish pursuits and self-centeredness, he leaves God almost completely out of his life. Still, he bears the name of God, attends Sabbath services, and at least in a superficial way, worships God on the Sabbath. Yet the relationship is growing cold as he fails to seek Him earnestly as in courtship.