"For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness, because what may be known of God is manifest in them, for God has shown it to them. For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse, because, although they knew God, they did not glorify Him as God, nor were thankful, but became futile in their thoughts, and their foolish hearts were darkened. Professing to be wise, they became fools, and changed the glory of the incorruptible God into an image made like corruptible man—and birds and four-footed animals and creeping things." (Romans 1:18-23).
If you're not already familiar with the argument, the chances are you have no idea how heretics use it as an argument against the Trinity. It's certainly not obvious, and of course it takes the passage wildly out of context. Perhaps, then, it is no wonder that it is rarely used by groups who so often rely on the exact words criteria. "Where does Jesus say 'I am God, worship me' in those exact words?" Well, where does Jesus say "I am not God, don't worship me" in those exact words?
The answer is certainly not in Romans 1. In fact, you will find several examples of people worshiping Jesus in Scripture - and He accepts. Take, for example, Matthew 2:11, 8:2, 9:18, 14:33, 15:25, and 28:9 and 17. But anti-Trinitarians do not use Romans 1:18-23 to suggest Jesus rejects worship. Rather, they use it to argue that, since there is nothing Triune in nature, God is also not Triune in nature.
There are three very obvious flaws with this argument, starting with the simple fact that is not what the verse is telling us at all. Although it talks about the nature of God being revealed through nature, it doesn't say literally everything about Him should be seen within it. In fact, the second obvious flaw is that if we took this interpretation to its logical conclusion, it would contradict the rest of Scripture. Scripture tells us multiple times that there is no one like God. Even the very will to be like God is the sin for which Satan was cast out of Heaven (Isaiah 14:14).
But the third obvious problem is that we don't need Scripture to tell us nothing is like God. Tell me, is there anything in nature that is subsistent? Eternal? Omniscient? Holy? There is nothing in nature that shares any of these attributes with God. How is it, then, that anti-Trinitarians use the fact that nothing in nature shares God's Triune nature as an argument against the Trinity? The only saving grace of this argument is its relative obscurity! Few people are silly enough to use it.
But there is a less obvious flaw: There is one thing in nature comparable to the Trinity. In fact, it is so comparable to the Trinity, it is one of His attributes. It is the one piece of Himself He placed into the creation before becoming incarnate through the blessed womb of a virgin. I am, of course, talking about love.
But how is love Triune? This isn't actually what I'm saying. Let's return to Romans 1 for a moment. Note how it says "...what may be known of God is manifest in them, for God has shown it to them. For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead...". Now, we cannot take this to its logical extreme. If God, who is from everlasting to everlasting, is the maker of everything that is made, then nothing in nature shares His eternal power. But is there power in nature? Certainly. If you're stupid enough, put your tongue on a fully charged 9v battery. From experience, I can tell you it's not pleasant...
So we can see that as long as a thing reflects an attribute of God, it meets the criteria. Now, love is an attribute of God, is it not? In fact, Scripture tells us that God is love (1 John 4:8)! But what is love, if it is not for another? A man who loves himself is not loving, but selfish, vain, and frankly not worthy of being loved. But love is true when it is directed elsewhere. A husband toward his wife, a wife towards her husband, parents towards their children, and children towards their parents.
Now obviously, I'm not going to say the Father is the husband, the Son is the wife, and the Holy Spirit is the child. That's taking it too literally, and too far. However, because love can only be expressed towards another, and God is love, there must always have been someone for Him to direct His love towards. But this necessitates a Trinity! It requires two members of Godhead to be reflected in how two love each other, and a third member to be reflected by the love two feel for one, but a fourth member of Godhead is redundant (not to mention contrary to Scripture).
Thus, while there is nothing in nature that is Triune, the Trinity is, nevertheless, reflected in nature. The only ways around this are to deny that God is love, that love is necessarily unselfish, or that God is subsistent. None of these conclusions are compatible with the Biblical God. Therefore, aside from this being one of the worst arguments you can make against the Trinity, it actually ends up being a fantastic argument in its favor.